Quantitative Business Analysis

Written assignments

6 & 7

College Algebra

Practice Exercises 7, 8, 9 & 10

Technology Activity 4 & 5

Offline download.zip

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Course Calendar

The Course Calendar provides an overview of assignment due dates and when to begin each module.

For details on each assignment, go to the course Web site and click the associated module.

Go to

Week-by-Week Dates

to see specific dates for the current semester.

Week 1

· Monday—

BEGIN MODULE 1

· Tuesday—

· Wednesday—Introductions Forum: 1st posting due

· Thursday—Discussion Forum 1: 1st posting due

· Friday—Introductions Forum: 2nd posting (comments) due

· Saturday—Discussion Forum 1: 2nd posting (comments) due

· Sunday—Written Assignment 1 due; Quiz 1 due

Week 2

· Monday—

BEGIN MODULE 2

· Tuesday—

· Wednesday—

· Thursday—Discussion Forum 2: 1st posting due

· Friday—

· Saturday—

· Sunday—

Week 3

· Monday—Discussion Forum 2: 2nd posting (comments) due

· Tuesday—

· Wednesday—Written Assignment 2 due; Quiz 2 due

· Thursday—

BEGIN MODULE 3

· Friday—

· Saturday—

· Sunday—Discussion Forum 3: 1st posting due

Week 4

· Monday—

· Tuesday—

· Wednesday—

· Thursday—

· Friday—Discussion Forum 3: 2nd posting (comments) due

· Saturday—

· Sunday—Written Assignment 3 due; Quiz 3 due

Week 5

· Monday—

BEGIN MODULE 4

· Tuesday—

· Wednesday—

· Thursday—Discussion Forum 4: 1st posting due

· Friday—

· Saturday—

· Sunday—

Week 6

· Monday—Discussion Forum 4: 2nd posting (comments) due

· Tuesday—

· Wednesday—Written Assignment 4 due; Quiz 4 due

· Thursday—

BEGIN MODULE 5

· Friday—

· Saturday—

· Sunday—Discussion Forum 5: 1st posting due

Week 7

· Monday—

· Tuesday—

· Wednesday—

· Thursday—

· Friday—Discussion Forum 5: 2nd posting (comments) due

· Saturday—

· Sunday—Written Assignment 5 due; Quiz 5 due

Week 8

· Monday—

BEGIN MODULE 6

· Tuesday—

· Wednesday—

· Thursday—Discussion Forum 6: 1st posting due

· Friday—

· Saturday—

· Sunday—

Week 9

· Monday—

· Tuesday—

· Wednesday—

· Thursday—

· Friday—Discussion Forum 6: 2nd posting (comments) due

· Saturday—

· Sunday—Written Assignment 6 due; Quiz 6 due

Week 10

· Monday—

BEGIN MODULE 7

· Tuesday—

· Wednesday—

· Thursday—Discussion Forum 7: 1st posting due

· Friday—

· Saturday—

· Sunday—

Week 11

· Monday—

· Tuesday—

· Wednesday—

· Thursday—

· Friday—Discussion Forum 7: 2nd posting (comments) due

· Saturday—

· Sunday—Written Assignment 7 due; Quiz 7 due

Week 12

Final Exam Week: Take exam by Sunday of Week 12.

· Monday—

· Tuesday—

· Wednesday—

· Thursday—

· Friday—

· Saturday—

· Sunday—

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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Syllabus for MAT-119

QUANTITATIVE BUSINESS ANALYSIS

COURSE DESCRIPTION

This is an applications-based course that continues with the mathematical inquiry that began in high school and intermediate algebra. This course prepares students for further study in business, finance, and management science. The underlying teaching philosophy is that students who study mathematics should develop alternate means of critical thinking and apply those means to the applications in the everyday business world. To this end, active participation is fostered by means of a variety of assignments. This provides the student with sophisticated computational skills while stressing the ability to think critically and objectively. These computational and thinking skills will be applied to a wide variety of business applications. Students are encouraged to explore and solve realistic applications in business, finance, and management science.

COURSE OBJECTIVES

After completing this course, you should be able to:

1. manipulate elementary algebraic expressions using basic mathematical knowledge

2. solve and graph linear equalities and inequalities

3. solve inequalities

4. evaluate functions using functional notation, domain, and range

5. solve applied problems using linear and quadratic functions

6. apply exponential and logarithmic functions to a variety of problems

7. calculate interest, discount, annuities, amortization payments, and balances

8. manipulate matrices

9. solve maximization and minimization problems.

COURSE MATERIALS

You will need the following materials to complete your coursework. Some course materials may be free, open source, or available from other providers. You can access free or open-source materials by clicking the links provided below or in the module details documents. To purchase course materials, please visit the

University’s textbook supplier

.

Required Textbook

· Lial, Margaret L., Hungerford, Thomas W., Holcomb, Jr., John P., and Mullins, Bernadette (2015).

Finite Mathematics with Applications in the Management, Natural, and Social Sciences (11th ed.). Boston, MA: Pearson.

ISBN-13: 9780321931061

Solutions Manual

· Lial, Margaret L., Hungerford, Thomas W., Holcomb, Jr., John P., and Mullins, Bernadette (2015).

Student Solutions Manual for Finite Mathematics with Applications In the Management, Natural and Social Sciences (11th ed.). Boston, MA: Pearson.

ISBN-13: 9780321986320

COURSE STRUCTURE

Quantitative Business Analysis is a three-credit online course, consisting of

seven modules. Modules include learning objectives, study materials, activities, and quizzes. Module titles are listed below.

·

Module 1: Review of Basic Concepts

·

Module 2: Linear Equations and Inequalities

·

Module 3: Functions and Their Linear and Quadratic Applications

·

Module 4: Exponential and Logarithmic Equations

·

Module 5: Business and Finance Applications

·

Module 6: Systems and Matrices

·

Module 7: Maximization and Minimization

ASSESSMENT METHODS

For your formal work in the course, you are required to participate in online discussion forums, complete written assignments, take quizzes, and a proctored online final examination. See below for more details.

Consult the Course Calendar for assignment due dates.

Promoting Originality

One or more of your course activities may utilize a tool designed to promote original work and evaluate your submissions for plagiarism. More information about this tool is available in

this document

.

Discussion Forums

You will have seven discussion forum assignments in this course. One per module. You are required to enter an initial response to the Discussion Question. In addition, you must post at least two responses to the initial response of other students and these two responses must be on different days during the module. This standard is a minimum requirement. It is suggested that you participate on a daily basis during the course.

Participation consists primarily of discussion the topic under consideration or other topics of interest regarding mathematics and its business applications. Participation is measured by a student’s meaningful contribution to the virtual classroom discussion. Only substantive contributions will be considered for grading. Notes such as “me too” and “I agree” and other notes not related to the course are not considered substantive notes for participation. A note is determined to be of substance by containing information that supplements, contradicts, questions, or furthers discussion on a subject area contained in the course.

Submitting assignments through the Assignment links, logging on and reading messages, posting messages in the “Lounge” or in the “Introduction,” and emails do not count towards participation.

Participation grading will, by necessity, be a combination of objective grading (number of postings) and subjectivity (quality of postings).

Written Assignments

You are required to complete

seven written assignments. The written assignments are on a variety of topics associated with the course modules.

Assignments must be prepared electronically with a word processor (e.g., Microsoft Word) and, preferably, whatever equation editor integrates with your word processing software. Since this is a course in mathematics, you are recommended to use an equation editor to place mathematical symbols in your work. (

Important: Use the equation editor only to insert equations into your word-processed document and not to create the document itself.) However, if your word processor is not compatible with your mentor’s word processor, you will need to save your document as a rich-text format (.rtf) file before submitting it. Check with your mentor first to determine file compatibility.

When preparing your answers, please identify each exercise clearly by textbook section and exercise number. Be sure to include your name at the top of the paper, as well as the course name and code and the semester and year in which you are enrolled. To receive full credit for your answers, you must show all work and include complete solutions. If you choose not to use an equation editor to write mathematical symbols, you’ll need to use the

Insert > Symbols menu of your word processor to find the appropriate symbols. Exponents can be inserted as superscripts using the

Format > Font menu.

Quizzes

There will be a quiz for each of the seven modules. The quizzes should be taken after you complete the practice exercises and the written assignment. There will be

five multiple-choice problems on each of the quizzes. You have up to

30 minutes in which to complete the quiz and may take it

only once.

Final Exam

The proctored, online final exam covers all reading and assignments from the course. The exam is three hours long. The final exam includes 50 multiple choice questions.

You may use your textbook as long as it doesn’t have any loose inserts. You are not allowed to bring or consult a solutions manual, notebook or notes of any kind, any practice or written assignment problems, or any other reference sources or sources of information.

Note:

You are permitted to use a calculator (scientific, graphing, or financial) but

may not

use a calculator on a phone, PDA, or any similar device.

For the final, you are required to use the University’s

Online Proctor Service

(OPS). Please refer to the “Examinations and Proctors” section of the Online Student Handbook (see

Student Handbooks

in the General Information area of the course website) for further information about scheduling and taking online exams and for all exam policies and procedures. You are strongly advised to schedule your exam within the first week of the semester.

Online exams are administered through the course Web site. Consult the Course Calendar for the official dates of exam weeks.

Statement about Cheating

You are on your honor not to cheat during an exam. Cheating means:

· Looking up any answer or part of an answer in an unauthorized textbook or on the Internet, or using any other source to find an answer.

· Copying and pasting or, in any way copying responses or parts of responses from any other source into your exams. This includes but is not limited to copying and pasting from other documents or spreadsheets, whether written by yourself or anyone else.

· Plagiarizing answers.

· Asking anyone else to assist you by whatever means available while you take an exam.

· Copying any part of an exam to share with other students.

· Telling your mentor that you need another attempt at an exam because your connection to the Internet was interrupted when that is not true.

If there is evidence that you have cheated or plagiarized in an exam, the exam will be declared invalid, and you will fail the course.

GRADING AND EVALUATION

Your grade in the course will be determined as follows:

·

Discussion Forums—20 percent

·

Written Assignments—30 percent

·

Quizzes—20 percent

·

Final exam (proctored online, modules 1-7)—30 percent

All activities will receive a numerical grade of 0–100. You will receive a score of 0 for any work not submitted. Your final grade in the course will be a letter grade. Letter grade equivalents for numerical grades are as follows:

A

=

93–100

C+

=

78–79

A–

=

90–92

C

=

73–77

B+

=

88–89

C–

=

70–72

B

=

83–87

D

=

60–69

B–

=

80–82

F

=

Below 60

To receive credit for the course, you must earn a letter grade of C or better (for an area of study course) or D or better (for a course not in your area of study), based on the weighted average of all assigned course work (e.g., exams, assignments, discussion postings, etc.).

STRATEGIES FOR SUCCESS

First Steps to Success

To succeed in this course, take the following first steps:

· Read carefully the entire Syllabus, making sure that all aspects of the course are clear to you and that you have all the materials required for the course.

· Take the time to read the entire Online Student Handbook. The Handbook answers many questions about how to proceed through the course, how to schedule exams, and how to get the most from your educational experience at Thomas Edison State University.

· Arrange to take your examinations by following the instructions in this Syllabus and the Online Student Handbook.

· Familiarize yourself with the learning management systems environment—how to navigate it and what the various course areas contain. If you know what to expect as you navigate the course, you can better pace yourself and complete the work on time.

· If you are not familiar with Web-based learning be sure to review the processes for posting responses online and submitting assignments before class begins.

Study Tips

Consider the following study tips for success:

· To stay on track throughout the course, begin each week by consulting the Course Calendar. The calendar provides an overview of the course and indicates due dates for submitting assignments, posting discussions, and scheduling and taking examinations.

· Read the module objectives. The module learning objectives provide a roadmap of sorts for your studies. As you complete each module, check that you have covered and achieved all the objectives.

· Read the study notes, and follow the examples. Study notes review, highlight, and summarize key concepts, terms, and applications from the module assignment. They are written with classroom notes in mind, the type of notes you would take if you were in a face-to-face classroom environment. The language is easy to understand, and the notes include examples that show problem solving step by step.

· Remember, practice makes perfect. The textbook has odd-numbered exercises very similar to the even-numbered exercises in your assignments. Answers to odd-numbered exercises are at the back of the textbook (solutions are in the optional

Student’s Solution Manual). It is good practice to solve some of the odd-numbered exercises before working on the written assignments.

· Check Announcements regularly for new course information.

ACADEMIC POLICIES

To ensure success in all your academic endeavors and coursework at Thomas Edison State University, familiarize yourself with all administrative and academic policies including those related to academic integrity, course late submissions, course extensions, and grading policies.

For more, see:

·

University-wide policies

·

Undergraduate course policies and regulations

·

Graduate academic policies

·

Nursing student policies

·

Academic code of conduct

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119 • Quantitative Business Analysis

Final Exam Study Guide

©2021 Thomas Edison State University

All Rights Reserved

Exam Details

Modules assessed: 1–7

Materials allowed: textbook, calculator

Duration: 3 hours

Exam Format

Multiple choice: 50 questions • 2 pts each • apply concepts to solve problems

Tips from the Test Development Team

·

How to Use the Study Guide to Help Prepare for Your Exam

·

How to Answer Multiple-Choice Questions

Chapter 1

· Adding and subtracting polynomial expressions

·

· Multiplying binomial expressions

· (5x – 7)(7x + 13)

· Factoring expressions completely

· x- 5x + 8

· 216a- 16b

· Multiplying rational expressions

·

· Adding rational expressions

·

· Simplifying expressions

·

· Solving equations

· 15y + 4 = 7y + 18

· Solving equations by factoring

· n+ 6n + 48 = 16

· Solving equations using the quadratic formula

· 4x+ 12x = -3

Chapter 2

· Finding x- and y-intercepts of an equation

· 5x + y = -3

· Representing equations with graphs

· y = x

· Finding slope and y-intercept of a line

· 8x + 12y = 15

· Finding the equation of a line with slope

m passing through a given point

· (4,6), m = 6

· Solving linear functions

· Suppose the sales of a particular brand of appliance satisfy the relationship S(x) = 200x + 4200, where S(x) represents the number of sales in year x, with x = 0 corresponding to 1997. Find the number of sales in 2009.

· Calculating the correlation coefficient r

· Consider the data points with the following coordinates:

x

22

16

15

18

21

y

3

5

6

9

4

· Solving inequalities

· > 0

Chapter 3

· Stating the domain of given functions

· y =

· Evaluating functions

· Find f(-3) when f(x) = x+ 7x + 2

· Solving linear cost and revenue functions

· At a manufacturing plant, the total cost (in dollars) to produce x items is C(x) = 5.35x + 21,000. What is the total cost to produce 100 items?

· Writing linear cost and revenue functions

· A limo service charges a flat fee of $100 plus $50 per hour. Let C(x) be the cost in dollars of using the limo service for x hours. Find the linear cost function.

· Determining the vertex of a parabola

· f(x) = x – 12x + 30

· Solving quadratic formulas

· Bill works at a car dealership. He has found that his salary (in dollars) is given by c(x) = 3x – 35x + 17, where x is the number of cars sold. What is his salary if the number of cars sold is 27?

Chapter 4

· Classifying functions as linear, quadratic, or exponential

· f(x) = x- 5

· Exponential growth and decay

· The number of bacteria growing in an incubation culture increases with time according to B(x) = 3000(2), where x is time in days. Find the number of bacteria when x = 0 and x = 4

· Find an exponential function of the form P(t) = ye

· A population of mice has an exponential growth rate of 13.7% per day. Consider an initial population of 100 mice. Find the exponential growth function.

· Population growth and decay word problems

· In a town whose population is 1000, a disease creates an epidemic. The number N of people infected t days after the disease has begun is given by the function

N(t) =

Find the number infected after 8 days.

· Writing expressions as logarithms of a single number or expression with a coefficient of 1

· log 12 – log 9

· 6 ln (x + 2) – 4 ln (x + 5)

· Solving logarithmic functions

· The height in meters of men of a certain tribe is approximated by h = 0.76 + 3log(t/5) where t is the man’s age in years and 1 ≤ t ≤ 35. Estimate the height (to the nearest hundredth of a meter) of a man of the tribe 19 years of age.

· Solving logarithmic and exponential equations

· log x = 11

· 5 = 814

· 8e = 11

Chapter 5

· Calculating interest

· Find the interest. Round to the nearest cent.

· $480 at 8% for 3 years

· Find the exact interest. Use 365 days in a year, and use the exact number of days in a month. Round to the nearest cent, if necessary.

· $7940 at 14.5% for 66 days

· Find the present value of the future amount. Assume 365 days in a year. Round to the nearest cent.

· $12,000 for 12 months; money earns 4%

· Find the actual interest rate paid, to the nearest tenth, on the simple discount note.

· $5000; discount rate 3.5%; length of loan 7 mo

· Calculating compound interest

· Find the compound amount for the deposit. Round to the nearest cent.

· $1200 at 6% compounded quarterly for 9 years

· Find the compound interest earned by the deposit. Round to the nearest cent.

· $18,000 at 3% compounded annually for 10 years

· Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated.

· $2500 at 12% compounded semiannually for 4 yr

· Calculating future value of annuities

· Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.

· R = $1200, i = 0.02, n = 8

· Calculating present value of annuities

· Find the present value of the ordinary annuity.

· Payments of $2200 made annually for 32 years at 11% compounded annually

· Amortizing loans

· Find the payment necessary to amortize the loan.

· $75,000; 9% compounded annually; 14 annual payments

· Find the monthly house payment necessary to amortize the following loan.

· In order to purchase a home, a family borrows $78,000 at 6.4% for 30 yrs. What is their monthly payment? Round the answer to the nearest cent.

Chapter 6

· Solving a system of equations

· x + 8y = 15 and 4x + 7y = 10

· Solve the system of equations. If the system is dependent, express solutions in terms of the parameter z.

x + y + z = -4

x – y + 3z = -6

4x + y + z = 5

· Solving a system of equations using the matrix method

· -x + 2y +5z = 1

3x – y – z = 2

x + 6y + 2z = 1

· Solving matrix equations

· Perform the indicated operation.

Let B = [-2 4 4 1] Find -3B

· Given the matrices A and B, find the matrix product AB.

A = B = Find AB

· Find the product.

· Find the inverse, if it exists, of the given matrix.

A =

Chapter 7

· Solving linear programming problems

· Use graphical methods to solve the linear programming problem.

Maximize z = 2x + 3y

subject to: 5x + 6y ≤ 10

x + 2y ≤ 6

x ≥ 0

y ≥ 0

· Use the simplex method to solve the linear programming problem.

Maximize z = 4x + 2x

subject to: 3x + 5x≤ 6

x + 2x≤ 15

with x≥ 0, x≥ 0

· Feasible regions of a system

· Describe the feasible region of x + y4 and x + y -16

· Maximization functions

· Convert the objective function into a maximization function.

Minimize w = 2y + 3y + 5y

subject to:

y + y ≥ 12

3y + 2y + y ≥ 26

y + 3y + y ≥ 8

y≥ 0, y≥ 0, y ≥ 0

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 4—Exponential and Logarithmic Equations

OBJECTIVES

After successfully completing Module 4, you should be able to:

· graph higher order polynomials

· graph rational functions

· graph exponential functions

· apply exponential functions

· graph logarithmic functions

· simplify logarithmic functions

· solve exponential functions

· solve logarithmic functions.

STUDY MATERIALS

Textbook Readings

· Study chapter 3, sections 3.5, 3.6 and chapter 4, sections 4.1, 4.2, 4.3, and 4.4 in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Work through the following practice exercises to review what you have learned in this module and also to help prepare for the written assignment and final exam. Check your work in the

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

Chapters 3 & 4

Section 3.5 Exercises

1, 3, 5, 7, 9, 13, 15, 27

Section 3.6 Exercises

1, 3, 11, 17, 27, 29, 31

Section 4.1 Exercises

1, 3, 5, 9, 13, 15, 19, 23, 25, 29, 35

Section 4.2 Exercises

1, 3, 7, 13, 19, 21

Section 4.3 Exercises

5, 7, 9, 13, 15, 23, 31, 35, 37, 41, 47, 53, 55

Section 4.4 Exercises

1, 3, 5, 7, 9, 13, 17, 19, 27, 31, 39, 41, 49, 53, 57, 63

ACTIVITIES

Module 4 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 4

In Discussion Forum 4, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Is the logarithmic function applicable when modeling business applications? Why or why not?

Written Assignment 4

The written assignment draws on even-numbered exercises from the textbook.

Answer all assigned exercises, and show all work.

Section

Exercises

3.5

2, 10, 14, 16, 36

3.6

2, 6, 18, 26

4.1

2, 4, 10, 20, 24, 26, 30, 36, 42, 46

4.2

2, 6, 12, 14, 20

4.3

6, 10, 14, 20, 30, 36, 38, 50, 54, 62

4.4

2, 4, 8, 14, 16, 24, 28, 36, 40, 46, 54, 58, 64

Assignments must be prepared electronically, using a word processor and whatever equation editor integrates with your word processing software. However, if your word processor is not compatible with your mentor’s word processor, you will need to save your document as a rich-text file (.rtf) before submitting it. Check with your mentor first to determine file compatibility.

When preparing your answers, please identify each exercise clearly by textbook section and exercise number. To receive full credit for your answers, you must show all work and include complete solutions.

Module 4 Quiz

The Module 4 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have completed all module assignments before you take the quiz.

Take the Module Quiz.

You have up to

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 4 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 5—Business and Finance Applications

OBJECTIVES

After successfully completing Module 5, you should be able to:

· calculate simple interest

· find the maturity value for simple interest

· find the present value for simple interest

· calculate discount

· calculate compound interest

· find the present value for compound interest

· calculate the future value of an ordinary annuity

· calculate the value of a sinking fund

· calculate annuities due

· calculate the present value of an annuity

· calculate amortization payments

· calculate the remaining balance.

STUDY MATERIALS

Textbook Readings

· Study chapter 5, sections 5.1, 5.2, 5.3, and 5.4, in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Work through the following practice exercises to review what you have learned in this module and also to help prepare for the written assignment and final exam. Check your work in the

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTER 5

Section 5.1 Exercises

3, 5, 9, 13, 17, 19, 25, 27, 33, 37, 41, 51

Section 5.2 Exercises

7, 9, 13, 19, 21, 23, 29, 31, 37, 41, 47, 51, 55

Section 5.3 Exercises

3, 5, 9, 15, 17, 21, 25, 27, 31, 35, 39, 41

Section 5.4 Exercises

3, 7, 11, 17, 25, 27, 31, 39, 41, 59,

ACTIVITIES

Module 5 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 5

In Discussion Forum 5, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Is it reasonable to allow home mortgages of, say 50 or 60 years? Think of this from the standpoint of the total amount paid after the loan has been completely paid off, from the view of the business, from the view of the customer.

Written Assignment 5

The written assignment draws on even-numbered exercises from the textbook.

Answer all assigned exercises, and show all work.

Section

Exercises

5.1

2, 4, 8, 18, 20, 24, 28, 36, 42, 50

5.2

8, 10, 14, 18, 22, 24, 28, 34, 36, 42, 50, 55, 64

5.3

4, 8, 10, 14, 20, 26, 28, 34, 42, 44

5.4

2, 8, 12, 16, 20, 28, 34, 40, 44, 50

Assignments must be prepared electronically, using a word processor and whatever equation editor integrates with your word processing software. However, if your word processor is not compatible with your mentor’s word processor, you will need to save your document as a rich-text file (.rtf) before submitting it. Check with your mentor first to determine file compatibility.

When preparing your answers, please identify each exercise clearly by textbook section and exercise number. To receive full credit for your answers, you must show all work and include complete solutions.

Module 5 Quiz

The Module 5 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have studied these sections carefully and have completed all module assignments before you take the quiz.

Take the Module Quiz.

You have up to

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 5 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 2—Linear Equations and Inequalities

OBJECTIVES

After successfully completing Module 2, you should be able to:

· identify solutions to equations

· find the x-intercepts and y-intercepts for equations

· sketch graphs

· interpret graphs

· calculate the slope of a line using two points

· find the slope-intercept form for a line

· determine whether two lines are parallel, perpendicular, or neither

· construct linear models

· find the least squares regression line

· solve linear inequalities

· graph linear inequalities.

STUDY MATERIALS

Textbook Readings

· Study chapter 2, sections 2.1, 2.2, 2.3, and 2.4, in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Work through the following practice exercises to review what you have learned in this module and also to help prepare for the written assignment and final exam. Check your work in the

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTER 2

Section 2.1 Exercises

1-47 (odd), 53, 54, 55, 56

Section 2.2 Exercises

1, 5, 7, 9, 15, 23, 25, 29, 37, 39, 43, 47, 53, 59, 63, 69

Section 2.3 Exercises

5, 7, 8, 12, 17

Section 2.4 Exercises

3-25 (odd); 29, 31, 33, 37, 41, 43, 47, 53

ACTIVITIES

Module 2 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 2

In Discussion Forum 2, post your response to the following discussion question topic. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

What are some of the shortcomings of the least squares regression line? Why do you consider these to be shortcomings? What can be done to compensate for them?

Written Assignment 2

The written assignment draws on even-numbered exercises from the textbook.

Answer all assigned exercises, and show all work.

Section

Exercises

2.1

4, 6, 16, 18, 26, 30, 40, 48, 78

2.2

4, 6, 14, 20, 24, 34, 36, 42, 46, 54, 58

2.3

6, 16, 18

2.4

4, 6, 14, 22, 24, 32, 36, 38, 40, 52

Assignments must be prepared electronically, using a word processor and whatever equation editor integrates with your word processing software. However, if your word processor is not compatible with your mentor’s word processor, you will need to save your document as a rich-text file (.rtf) before submitting it. Check with your mentor first to determine file compatibility.

When preparing your answers, please identify each exercise clearly by textbook section and exercise number. To receive full credit for your answers, you must show all work and include complete solutions.

Module 2 Quiz

The module 2 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have completed all module assignments before you take the quiz.

Take the Module Quiz.

You have up to

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 2 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 3—Functions and Their Linear and Quadratic Applications

OBJECTIVES

After successfully completing Module 3, you should be able to:

· solve polynomial inequalities

· solve rational inequalities

· graph polynomial inequalities

· identify a function

· find the domain and range of a function

· evaluate a function at a given value

· graph functions

· apply linear functions to solve problems

· find the vertex of a quadratic function

· graph quadratic functions

· apply quadratic functions to solve problems.

STUDY MATERIALS

Textbook Readings

· Study chapter 2, section 2.5, and chapter 3, sections 3.1, 3.2, 3.3, and 3.4 in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTERS 2 & 3

Section 2.5 Exercises

1, 3, 7, 9, 11, 15, 17, 29, 31, 35, 43

Section 3.1 Exercises

1, 3, 7, 9, 11, 15, 19, 27, 29, 35, 41, 49

Section 3.2 Exercises

1, 5, 7, 9, 13, 17, 27, 31, 57

Section 3.3 Exercises

1, 3, 5, 7, 9, 17, 19, 33, 35, 43

Section 3.4 Exercises

13, 15, 17, 19, 29, 35, 37, 39, 41, 51

ACTIVITIES

Module 3 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 3

In Discussion Forum 3, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

The concept of “market equilibrium” is defined as when the quantity of a commodity demanded is equal to the quantity supplied. Assume that the demand function and the supply function are both linear. How can good advertising affect market equilibrium? How can bad advertising affect market equilibrium?

Written Assignment 3

Answer all assigned exercises, and show all work.

Section

Exercises

2.5

2, 4, 8, 12, 16, 20, 36

3.1

2, 6, 8, 12, 16, 22, 24, 32, 34, 44, 50

3.2

2, 6, 14, 30, 48, 52

3.3

2, 6, 10, 16, 18, 34, 42, 50

3.4

14, 16, 22, 30, 32, 38, 40, 42, 52, 54

Module 3 Quiz

The module 3 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 3 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 1—Review of Basic Concepts

OBJECTIVES

After successfully completing Module 1, you should be able to:

· add, subtract, and multiply polynomials

· factor polynomials

· simplify rational expressions

· add, subtract, and multiply rational expressions

· simplify expressions with exponents

· add, subtract, and multiply radical expressions

· solve linear equations

· solve quadratic equations.

STUDY MATERIALS

Textbook Readings

· Study chapter 1, sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, and 1.7, in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Work through the following practice exercises to review what you have learned in this module and also to help prepare for the written assignments and final exam. Check your work in the

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTER 1

Section 1.2 Exercises

17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39

Section 1.3 Exercises

1, 3, 7, 9, 11, 23, 31, 37, 43, 53, 57, 77

Section 1.4 Exercises

1, 5, 9, 15, 19, 23, 31, 39, 45

Section 1.5 Exercises

1, 5, 9, 15, 23, 27, 37, 43, 55, 71, 75

Section 1.6 Exercises

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 29, 31

Section 1.7 Exercises

1, 3, 7, 11, 15, 21, 23, 25, 29, 31, 35, 37, 43, 45

ACTIVITIES

Module 1 has four activities. Please consult the Course Calendar for the due dates.

Introductions Forum

In the Introductions forum, please address any of the following topics or anything about yourself that you would like to share with the class so that we can get to know you better.

· Your reasons for taking this course

· Your interest in mathematics

· Your background in general

· Your experience with online learning

· Your expectations from this course

Note: The Introductions Forum is not graded but required.

Discussion Forum 1

In Discussion Forum 1, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Examine the role of mathematics that men and women in business, industry, and management use to make decisions that affect the success or failure of their efforts. How can mathematics help them make better decision? How can mathematics help them increase their chances for success?

Written Assignment 1

Answer all assigned exercises, and show all work.

Section

Exercises

1.2

18, 22, 24, 32

1.3

2, 6, 24, 26, 32, 58, 72

1.4

8, 12, 22, 40, 42

1.5

2, 6, 12, 20, 32, 48, 68, 74

1.6

2, 6, 8, 10, 14, 18, 24, 30

1.7

2, 4, 8, 10, 14, 16, 22, 36, 38, 46

Module 1 Quiz

The module 1 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 1 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 7—Maximization and Minimization

OBJECTIVES

After successfully completing Module 7, you should be able to:

· solve linear programming applications using the graphical method

· solve maximization problems using the simplex method

· solve minimization problems using the simplex method

· apply the simplex method to nonstandard problems.

STUDY MATERIALS

Textbook Readings

· Study chapter 7, sections 7.2, 7.3, 7.4, 7.5, 7.6, and 7.7 in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTER 7

Section 7.2 Exercises

1, 3, 7, 13, 15, 17

Section 7.3 Exercises

1, 3, 13, 19, 23

Section 7.4 Exercises

1, 5, 7, 11, 13, 17, 19, 27, 31

Section 7.5 Exercises

1, 5, 11, 13

Section 7.6 Exercises

1, 5, 17, 25, 29, 33

Section 7.7 Exercises

1, 5, 9, 13, 29, 35

ACTIVITIES

Module 7 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 7

In Discussion Forum 7, post your response to the following discussion topic. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Discuss the role of maximization and minimization in business.

Written Assignment 7

Answer all assigned exercises, and show all work.

Section

Exercises

7.2

2, 6, 8, 14, 16

7.3

2, 8, 18, 24

7.4

2, 8, 12, 14, 18, 20, 26, 30, 34

7.5

2, 8, 12

7.6

2, 6, 10, 20, 28, 32

7.7

2, 6, 10, 16, 30, 38

Assignment must be prepared electronically, using a word processor and whatever equation editor integrates with your word processing software. However, if your word processor is not compatible with your mentor’s word processor, you will need to save your document as a rich-text file (.rtf) before submitting it. Check with your mentor first to determine file compatibility.

Module 7 Quiz

The Module 7 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have studied these sections carefully and have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 7 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 6—Systems and Matrices

OBJECTIVES

After successfully completing Module 6, you should be able to:

· solve systems of linear equations

· add and subtract matrices

· multiply matrices

· find the inverse of a matrix

· apply matrix theory to solve problems

· graph linear inequalities in with two variables.

STUDY MATERIALS

Textbook Readings

· Study chapter 6, sections 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 and chapter 7, section 7.1 in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTERS 6 & 7

Section 6.1 Exercises

3, 5, 7, 11, 15, 23

Section 6.2 Exercises

13, 15, 31, 37

Section 6.3 Exercises

9, 11

Section 6.4 Exercises

1, 3, 9, 11, 15, 19, 31, 35

Section 6.5 Exercises

1, 5, 9, 11, 17, 31, 39, 55

Section 6.6 Exercises

1, 5, 7, 11, 17, 25, 37

Section 7.1 Exercises

1, 3, 5, 7, 11, 17, 23, 25, 33, 39, 45

ACTIVITIES

Module 6 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 6

In Discussion Forum 6, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Read Case Study 6 “Matrix Operations and Airline Route Maps” on pp. 334-345 of the textbook, paying special attention to adjacency matrices. How can such matrices help business conduct its day-to-day affairs?

Written Assignment 6

Answer all assigned exercises, and show all work.

Section

Exercises

6.1

4, 6, 10, 14, 20, 30

6.2

14, 16, 32, 38

6.3

10, 12

6.4

2, 10, 14, 18, 32, 36

6.5

2, 6, 10, 16, 30, 34, 40, 56

6.6

2, 6, 10, 12, 20, 34

7.1

2, 6, 8, 16, 22, 30, 34, 52, 54

Module 6 Quiz

The Module 6 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have studied these sections carefully and have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 6 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Course Calendar

The Course Calendar provides an overview of assignment due dates and when to begin each module.

For details on each assignment, go to the course Web site and click the associated module.

Go to

Week-by-Week Dates

to see specific dates for the current semester.

Week 1

· Monday—

BEGIN MODULE 1

· Tuesday—

· Wednesday—Introductions Forum: 1st posting due

· Thursday—Discussion Forum 1: 1st posting due

· Friday—Introductions Forum: 2nd posting (comments) due

· Saturday—Discussion Forum 1: 2nd posting (comments) due

· Sunday—Written Assignment 1 due; Quiz 1 due

Week 2

· Monday—

BEGIN MODULE 2

· Tuesday—

· Wednesday—

· Thursday—Discussion Forum 2: 1st posting due

· Friday—

· Saturday—

· Sunday—

Week 3

· Monday—Discussion Forum 2: 2nd posting (comments) due

· Tuesday—

· Wednesday—Written Assignment 2 due; Quiz 2 due

· Thursday—

BEGIN MODULE 3

· Friday—

· Saturday—

· Sunday—Discussion Forum 3: 1st posting due

Week 4

· Monday—

· Tuesday—

· Wednesday—

· Thursday—

· Friday—Discussion Forum 3: 2nd posting (comments) due

· Saturday—

· Sunday—Written Assignment 3 due; Quiz 3 due

Week 5

· Monday—

BEGIN MODULE 4

· Tuesday—

· Wednesday—

· Thursday—Discussion Forum 4: 1st posting due

· Friday—

· Saturday—

· Sunday—

Week 6

· Monday—Discussion Forum 4: 2nd posting (comments) due

· Tuesday—

· Wednesday—Written Assignment 4 due; Quiz 4 due

· Thursday—

BEGIN MODULE 5

· Friday—

· Saturday—

· Sunday—Discussion Forum 5: 1st posting due

Week 7

· Monday—

· Tuesday—

· Wednesday—

· Thursday—

· Friday—Discussion Forum 5: 2nd posting (comments) due

· Saturday—

· Sunday—Written Assignment 5 due; Quiz 5 due

Week 8

· Monday—

BEGIN MODULE 6

· Tuesday—

· Wednesday—

· Thursday—Discussion Forum 6: 1st posting due

· Friday—

· Saturday—

· Sunday—

Week 9

· Monday—

· Tuesday—

· Wednesday—

· Thursday—

· Friday—Discussion Forum 6: 2nd posting (comments) due

· Saturday—

· Sunday—Written Assignment 6 due; Quiz 6 due

Week 10

· Monday—

BEGIN MODULE 7

· Tuesday—

· Wednesday—

· Thursday—Discussion Forum 7: 1st posting due

· Friday—

· Saturday—

· Sunday—

Week 11

· Monday—

· Tuesday—

· Wednesday—

· Thursday—

· Friday—Discussion Forum 7: 2nd posting (comments) due

· Saturday—

· Sunday—Written Assignment 7 due; Quiz 7 due

Week 12

Final Exam Week: Take exam by Sunday of Week 12.

· Monday—

· Tuesday—

· Wednesday—

· Thursday—

· Friday—

· Saturday—

· Sunday—

Copyright © 2016 by Thomas Edison State University. All rights reserved.

exam study guides_15apr/final exam study guide_MAT-119-apr15 x

MAT-119 • Quantitative Business Analysis

Final Exam Study Guide

©2021 Thomas Edison State University

All Rights Reserved

Exam Details

Modules assessed: 1–7

Materials allowed: textbook, calculator

Duration: 3 hours

Exam Format

Multiple choice: 50 questions • 2 pts each • apply concepts to solve problems

Tips from the Test Development Team

·

How to Use the Study Guide to Help Prepare for Your Exam

·

How to Answer Multiple-Choice Questions

Chapter 1

· Adding and subtracting polynomial expressions

·

· Multiplying binomial expressions

· (5x – 7)(7x + 13)

· Factoring expressions completely

· x- 5x + 8

· 216a- 16b

· Multiplying rational expressions

·

· Adding rational expressions

·

· Simplifying expressions

·

· Solving equations

· 15y + 4 = 7y + 18

· Solving equations by factoring

· n+ 6n + 48 = 16

· Solving equations using the quadratic formula

· 4x+ 12x = -3

Chapter 2

· Finding x- and y-intercepts of an equation

· 5x + y = -3

· Representing equations with graphs

· y = x

· Finding slope and y-intercept of a line

· 8x + 12y = 15

· Finding the equation of a line with slope

m passing through a given point

· (4,6), m = 6

· Solving linear functions

· Suppose the sales of a particular brand of appliance satisfy the relationship S(x) = 200x + 4200, where S(x) represents the number of sales in year x, with x = 0 corresponding to 1997. Find the number of sales in 2009.

· Calculating the correlation coefficient r

· Consider the data points with the following coordinates:

x

22

16

15

18

21

y

3

5

6

9

4

· Solving inequalities

· > 0

Chapter 3

· Stating the domain of given functions

· y =

· Evaluating functions

· Find f(-3) when f(x) = x+ 7x + 2

· Solving linear cost and revenue functions

· At a manufacturing plant, the total cost (in dollars) to produce x items is C(x) = 5.35x + 21,000. What is the total cost to produce 100 items?

· Writing linear cost and revenue functions

· A limo service charges a flat fee of $100 plus $50 per hour. Let C(x) be the cost in dollars of using the limo service for x hours. Find the linear cost function.

· Determining the vertex of a parabola

· f(x) = x – 12x + 30

· Solving quadratic formulas

· Bill works at a car dealership. He has found that his salary (in dollars) is given by c(x) = 3x – 35x + 17, where x is the number of cars sold. What is his salary if the number of cars sold is 27?

Chapter 4

· Classifying functions as linear, quadratic, or exponential

· f(x) = x- 5

· Exponential growth and decay

· The number of bacteria growing in an incubation culture increases with time according to B(x) = 3000(2), where x is time in days. Find the number of bacteria when x = 0 and x = 4

· Find an exponential function of the form P(t) = ye

· A population of mice has an exponential growth rate of 13.7% per day. Consider an initial population of 100 mice. Find the exponential growth function.

· Population growth and decay word problems

· In a town whose population is 1000, a disease creates an epidemic. The number N of people infected t days after the disease has begun is given by the function

N(t) =

Find the number infected after 8 days.

· Writing expressions as logarithms of a single number or expression with a coefficient of 1

· log 12 – log 9

· 6 ln (x + 2) – 4 ln (x + 5)

· Solving logarithmic functions

· The height in meters of men of a certain tribe is approximated by h = 0.76 + 3log(t/5) where t is the man’s age in years and 1 ≤ t ≤ 35. Estimate the height (to the nearest hundredth of a meter) of a man of the tribe 19 years of age.

· Solving logarithmic and exponential equations

· log x = 11

· 5 = 814

· 8e = 11

Chapter 5

· Calculating interest

· Find the interest. Round to the nearest cent.

· $480 at 8% for 3 years

· Find the exact interest. Use 365 days in a year, and use the exact number of days in a month. Round to the nearest cent, if necessary.

· $7940 at 14.5% for 66 days

· Find the present value of the future amount. Assume 365 days in a year. Round to the nearest cent.

· $12,000 for 12 months; money earns 4%

· Find the actual interest rate paid, to the nearest tenth, on the simple discount note.

· $5000; discount rate 3.5%; length of loan 7 mo

· Calculating compound interest

· Find the compound amount for the deposit. Round to the nearest cent.

· $1200 at 6% compounded quarterly for 9 years

· Find the compound interest earned by the deposit. Round to the nearest cent.

· $18,000 at 3% compounded annually for 10 years

· Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated.

· $2500 at 12% compounded semiannually for 4 yr

· Calculating future value of annuities

· Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.

· R = $1200, i = 0.02, n = 8

· Calculating present value of annuities

· Find the present value of the ordinary annuity.

· Payments of $2200 made annually for 32 years at 11% compounded annually

· Amortizing loans

· Find the payment necessary to amortize the loan.

· $75,000; 9% compounded annually; 14 annual payments

· Find the monthly house payment necessary to amortize the following loan.

· In order to purchase a home, a family borrows $78,000 at 6.4% for 30 yrs. What is their monthly payment? Round the answer to the nearest cent.

Chapter 6

· Solving a system of equations

· x + 8y = 15 and 4x + 7y = 10

· Solve the system of equations. If the system is dependent, express solutions in terms of the parameter z.

x + y + z = -4

x – y + 3z = -6

4x + y + z = 5

· Solving a system of equations using the matrix method

· -x + 2y +5z = 1

3x – y – z = 2

x + 6y + 2z = 1

· Solving matrix equations

· Perform the indicated operation.

Let B = [-2 4 4 1] Find -3B

· Given the matrices A and B, find the matrix product AB.

A = B = Find AB

· Find the product.

· Find the inverse, if it exists, of the given matrix.

A =

Chapter 7

· Solving linear programming problems

· Use graphical methods to solve the linear programming problem.

Maximize z = 2x + 3y

subject to: 5x + 6y ≤ 10

x + 2y ≤ 6

x ≥ 0

y ≥ 0

· Use the simplex method to solve the linear programming problem.

Maximize z = 4x + 2x

subject to: 3x + 5x≤ 6

x + 2x≤ 15

with x≥ 0, x≥ 0

· Feasible regions of a system

· Describe the feasible region of x + y4 and x + y -16

· Maximization functions

· Convert the objective function into a maximization function.

Minimize w = 2y + 3y + 5y

subject to:

y + y ≥ 12

3y + 2y + y ≥ 26

y + 3y + y ≥ 8

y≥ 0, y≥ 0, y ≥ 0

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 1—Review of Basic Concepts

OBJECTIVES

After successfully completing Module 1, you should be able to:

· add, subtract, and multiply polynomials

· factor polynomials

· simplify rational expressions

· add, subtract, and multiply rational expressions

· simplify expressions with exponents

· add, subtract, and multiply radical expressions

· solve linear equations

· solve quadratic equations.

STUDY MATERIALS

Textbook Readings

· Study chapter 1, sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, and 1.7, in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Work through the following practice exercises to review what you have learned in this module and also to help prepare for the written assignments and final exam. Check your work in the

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTER 1

Section 1.2 Exercises

17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39

Section 1.3 Exercises

1, 3, 7, 9, 11, 23, 31, 37, 43, 53, 57, 77

Section 1.4 Exercises

1, 5, 9, 15, 19, 23, 31, 39, 45

Section 1.5 Exercises

1, 5, 9, 15, 23, 27, 37, 43, 55, 71, 75

Section 1.6 Exercises

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 29, 31

Section 1.7 Exercises

1, 3, 7, 11, 15, 21, 23, 25, 29, 31, 35, 37, 43, 45

ACTIVITIES

Module 1 has four activities. Please consult the Course Calendar for the due dates.

Introductions Forum

In the Introductions forum, please address any of the following topics or anything about yourself that you would like to share with the class so that we can get to know you better.

· Your reasons for taking this course

· Your interest in mathematics

· Your background in general

· Your experience with online learning

· Your expectations from this course

Note: The Introductions Forum is not graded but required.

Discussion Forum 1

In Discussion Forum 1, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Examine the role of mathematics that men and women in business, industry, and management use to make decisions that affect the success or failure of their efforts. How can mathematics help them make better decision? How can mathematics help them increase their chances for success?

Written Assignment 1

Answer all assigned exercises, and show all work.

Section

Exercises

1.2

18, 22, 24, 32

1.3

2, 6, 24, 26, 32, 58, 72

1.4

8, 12, 22, 40, 42

1.5

2, 6, 12, 20, 32, 48, 68, 74

1.6

2, 6, 8, 10, 14, 18, 24, 30

1.7

2, 4, 8, 10, 14, 16, 22, 36, 38, 46

Module 1 Quiz

The module 1 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 1 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 2—Linear Equations and Inequalities

OBJECTIVES

After successfully completing Module 2, you should be able to:

· identify solutions to equations

· find the x-intercepts and y-intercepts for equations

· sketch graphs

· interpret graphs

· calculate the slope of a line using two points

· find the slope-intercept form for a line

· determine whether two lines are parallel, perpendicular, or neither

· construct linear models

· find the least squares regression line

· solve linear inequalities

· graph linear inequalities.

STUDY MATERIALS

Textbook Readings

· Study chapter 2, sections 2.1, 2.2, 2.3, and 2.4, in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTER 2

Section 2.1 Exercises

1-47 (odd), 53, 54, 55, 56

Section 2.2 Exercises

1, 5, 7, 9, 15, 23, 25, 29, 37, 39, 43, 47, 53, 59, 63, 69

Section 2.3 Exercises

5, 7, 8, 12, 17

Section 2.4 Exercises

3-25 (odd); 29, 31, 33, 37, 41, 43, 47, 53

ACTIVITIES

Module 2 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 2

In Discussion Forum 2, post your response to the following discussion question topic. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

What are some of the shortcomings of the least squares regression line? Why do you consider these to be shortcomings? What can be done to compensate for them?

Written Assignment 2

Answer all assigned exercises, and show all work.

Section

Exercises

2.1

4, 6, 16, 18, 26, 30, 40, 48, 78

2.2

4, 6, 14, 20, 24, 34, 36, 42, 46, 54, 58

2.3

6, 16, 18

2.4

4, 6, 14, 22, 24, 32, 36, 38, 40, 52

Module 2 Quiz

The module 2 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 2 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 3—Functions and Their Linear and Quadratic Applications

OBJECTIVES

After successfully completing Module 3, you should be able to:

· solve polynomial inequalities

· solve rational inequalities

· graph polynomial inequalities

· identify a function

· find the domain and range of a function

· evaluate a function at a given value

· graph functions

· apply linear functions to solve problems

· find the vertex of a quadratic function

· graph quadratic functions

· apply quadratic functions to solve problems.

STUDY MATERIALS

Textbook Readings

· Study chapter 2, section 2.5, and chapter 3, sections 3.1, 3.2, 3.3, and 3.4 in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTERS 2 & 3

Section 2.5 Exercises

1, 3, 7, 9, 11, 15, 17, 29, 31, 35, 43

Section 3.1 Exercises

1, 3, 7, 9, 11, 15, 19, 27, 29, 35, 41, 49

Section 3.2 Exercises

1, 5, 7, 9, 13, 17, 27, 31, 57

Section 3.3 Exercises

1, 3, 5, 7, 9, 17, 19, 33, 35, 43

Section 3.4 Exercises

13, 15, 17, 19, 29, 35, 37, 39, 41, 51

ACTIVITIES

Module 3 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 3

In Discussion Forum 3, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

The concept of “market equilibrium” is defined as when the quantity of a commodity demanded is equal to the quantity supplied. Assume that the demand function and the supply function are both linear. How can good advertising affect market equilibrium? How can bad advertising affect market equilibrium?

Written Assignment 3

Answer all assigned exercises, and show all work.

Section

Exercises

2.5

2, 4, 8, 12, 16, 20, 36

3.1

2, 6, 8, 12, 16, 22, 24, 32, 34, 44, 50

3.2

2, 6, 14, 30, 48, 52

3.3

2, 6, 10, 16, 18, 34, 42, 50

3.4

14, 16, 22, 30, 32, 38, 40, 42, 52, 54

Module 3 Quiz

The module 3 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 3 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 4—Exponential and Logarithmic Equations

OBJECTIVES

After successfully completing Module 4, you should be able to:

· graph higher order polynomials

· graph rational functions

· graph exponential functions

· apply exponential functions

· graph logarithmic functions

· simplify logarithmic functions

· solve exponential functions

· solve logarithmic functions.

STUDY MATERIALS

Textbook Readings

· Study chapter 3, sections 3.5, 3.6 and chapter 4, sections 4.1, 4.2, 4.3, and 4.4 in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

Chapters 3 & 4

Section 3.5 Exercises

1, 3, 5, 7, 9, 13, 15, 27

Section 3.6 Exercises

1, 3, 11, 17, 27, 29, 31

Section 4.1 Exercises

1, 3, 5, 9, 13, 15, 19, 23, 25, 29, 35

Section 4.2 Exercises

1, 3, 7, 13, 19, 21

Section 4.3 Exercises

5, 7, 9, 13, 15, 23, 31, 35, 37, 41, 47, 53, 55

Section 4.4 Exercises

1, 3, 5, 7, 9, 13, 17, 19, 27, 31, 39, 41, 49, 53, 57, 63

ACTIVITIES

Module 4 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 4

In Discussion Forum 4, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Is the logarithmic function applicable when modeling business applications? Why or why not?

Written Assignment 4

Answer all assigned exercises, and show all work.

Section

Exercises

3.5

2, 10, 14, 16, 36

3.6

2, 6, 18, 26

4.1

2, 4, 10, 20, 24, 26, 30, 36, 42, 46

4.2

2, 6, 12, 14, 20

4.3

6, 10, 14, 20, 30, 36, 38, 50, 54, 62

4.4

2, 4, 8, 14, 16, 24, 28, 36, 40, 46, 54, 58, 64

Module 4 Quiz

The Module 4 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 4 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 5—Business and Finance Applications

OBJECTIVES

After successfully completing Module 5, you should be able to:

· calculate simple interest

· find the maturity value for simple interest

· find the present value for simple interest

· calculate discount

· calculate compound interest

· find the present value for compound interest

· calculate the future value of an ordinary annuity

· calculate the value of a sinking fund

· calculate annuities due

· calculate the present value of an annuity

· calculate amortization payments

· calculate the remaining balance.

STUDY MATERIALS

Textbook Readings

· Study chapter 5, sections 5.1, 5.2, 5.3, and 5.4, in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTER 5

Section 5.1 Exercises

3, 5, 9, 13, 17, 19, 25, 27, 33, 37, 41, 51

Section 5.2 Exercises

7, 9, 13, 19, 21, 23, 29, 31, 37, 41, 47, 51, 55

Section 5.3 Exercises

3, 5, 9, 15, 17, 21, 25, 27, 31, 35, 39, 41

Section 5.4 Exercises

3, 7, 11, 17, 25, 27, 31, 39, 41, 59,

ACTIVITIES

Module 5 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 5

In Discussion Forum 5, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Is it reasonable to allow home mortgages of, say 50 or 60 years? Think of this from the standpoint of the total amount paid after the loan has been completely paid off, from the view of the business, from the view of the customer.

Written Assignment 5

Answer all assigned exercises, and show all work.

Section

Exercises

5.1

2, 4, 8, 18, 20, 24, 28, 36, 42, 50

5.2

8, 10, 14, 18, 22, 24, 28, 34, 36, 42, 50, 55, 64

5.3

4, 8, 10, 14, 20, 26, 28, 34, 42, 44

5.4

2, 8, 12, 16, 20, 28, 34, 40, 44, 50

Module 5 Quiz

The Module 5 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have studied these sections carefully and have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 5 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 6—Systems and Matrices

OBJECTIVES

After successfully completing Module 6, you should be able to:

· solve systems of linear equations

· add and subtract matrices

· multiply matrices

· find the inverse of a matrix

· apply matrix theory to solve problems

· graph linear inequalities in with two variables.

STUDY MATERIALS

Textbook Readings

· Study chapter 6, sections 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 and chapter 7, section 7.1 in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTERS 6 & 7

Section 6.1 Exercises

3, 5, 7, 11, 15, 23

Section 6.2 Exercises

13, 15, 31, 37

Section 6.3 Exercises

9, 11

Section 6.4 Exercises

1, 3, 9, 11, 15, 19, 31, 35

Section 6.5 Exercises

1, 5, 9, 11, 17, 31, 39, 55

Section 6.6 Exercises

1, 5, 7, 11, 17, 25, 37

Section 7.1 Exercises

1, 3, 5, 7, 11, 17, 23, 25, 33, 39, 45

ACTIVITIES

Module 6 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 6

In Discussion Forum 6, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Read Case Study 6 “Matrix Operations and Airline Route Maps” on pp. 334-345 of the textbook, paying special attention to adjacency matrices. How can such matrices help business conduct its day-to-day affairs?

Written Assignment 6

Answer all assigned exercises, and show all work.

Section

Exercises

6.1

4, 6, 10, 14, 20, 30

6.2

14, 16, 32, 38

6.3

10, 12

6.4

2, 10, 14, 18, 32, 36

6.5

2, 6, 10, 16, 30, 34, 40, 56

6.6

2, 6, 10, 12, 20, 34

7.1

2, 6, 8, 16, 22, 30, 34, 52, 54

Module 6 Quiz

The Module 6 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have studied these sections carefully and have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 6 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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MAT-119: QUANTITATIVE BUSINESS ANALYSIS

Module 7—Maximization and Minimization

OBJECTIVES

After successfully completing Module 7, you should be able to:

· solve linear programming applications using the graphical method

· solve maximization problems using the simplex method

· solve minimization problems using the simplex method

· apply the simplex method to nonstandard problems.

STUDY MATERIALS

Textbook Readings

· Study chapter 7, sections 7.2, 7.3, 7.4, 7.5, 7.6, and 7.7 in

Finite Mathematics with Applications, by Lial, Hungerford, Holcomb, and Mullins.

Practice Exercises

Student’s Solutions Manual.

Do not submit your solutions to your mentor.

CHAPTER 7

Section 7.2 Exercises

1, 3, 7, 13, 15, 17

Section 7.3 Exercises

1, 3, 13, 19, 23

Section 7.4 Exercises

1, 5, 7, 11, 13, 17, 19, 27, 31

Section 7.5 Exercises

1, 5, 11, 13

Section 7.6 Exercises

1, 5, 17, 25, 29, 33

Section 7.7 Exercises

1, 5, 9, 13, 29, 35

ACTIVITIES

Module 7 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 7

In Discussion Forum 7, post your response to the following discussion topic. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Discuss the role of maximization and minimization in business.

Written Assignment 7

Answer all assigned exercises, and show all work.

Section

Exercises

7.2

2, 6, 8, 14, 16

7.3

2, 8, 18, 24

7.4

2, 8, 12, 14, 18, 20, 26, 30, 34

7.5

2, 8, 12

7.6

2, 6, 10, 20, 28, 32

7.7

2, 6, 10, 16, 30, 38

Assignment must be prepared electronically, using a word processor and whatever equation editor integrates with your word processing software. However, if your word processor is not compatible with your mentor’s word processor, you will need to save your document as a rich-text file (.rtf) before submitting it. Check with your mentor first to determine file compatibility.

Module 7 Quiz

The Module 7 quiz consists of

five questions that are similar to the questions in the exercises, but in multiple-choice format. Be sure you have studied these sections carefully and have completed all module assignments before you take the quiz.

Take the Module Quiz.

30 minutes to complete the online quiz and may take it

only once. Please set aside sufficient time to complete the quiz, since once you quit the quiz or time has expired, the quiz will not allow you to re-enter at a later time.

Consult the Course Calendar for the Module 7 Quiz deadline.

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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Syllabus for MAT-119

QUANTITATIVE BUSINESS ANALYSIS

COURSE DESCRIPTION

This is an applications-based course that continues with the mathematical inquiry that began in high school and intermediate algebra. This course prepares students for further study in business, finance, and management science. The underlying teaching philosophy is that students who study mathematics should develop alternate means of critical thinking and apply those means to the applications in the everyday business world. To this end, active participation is fostered by means of a variety of assignments. This provides the student with sophisticated computational skills while stressing the ability to think critically and objectively. These computational and thinking skills will be applied to a wide variety of business applications. Students are encouraged to explore and solve realistic applications in business, finance, and management science.

COURSE OBJECTIVES

After completing this course, you should be able to:

1. manipulate elementary algebraic expressions using basic mathematical knowledge

2. solve and graph linear equalities and inequalities

3. solve inequalities

4. evaluate functions using functional notation, domain, and range

5. solve applied problems using linear and quadratic functions

6. apply exponential and logarithmic functions to a variety of problems

7. calculate interest, discount, annuities, amortization payments, and balances

8. manipulate matrices

9. solve maximization and minimization problems.

COURSE MATERIALS

You will need the following materials to complete your coursework. Some course materials may be free, open source, or available from other providers. You can access free or open-source materials by clicking the links provided below or in the module details documents. To purchase course materials, please visit the

University’s textbook supplier

.

Required Textbook

· Lial, Margaret L., Hungerford, Thomas W., Holcomb, Jr., John P., and Mullins, Bernadette (2015).

Finite Mathematics with Applications in the Management, Natural, and Social Sciences (11th ed.). Boston, MA: Pearson.

ISBN-13: 9780321931061

Solutions Manual

· Lial, Margaret L., Hungerford, Thomas W., Holcomb, Jr., John P., and Mullins, Bernadette (2015).

Student Solutions Manual for Finite Mathematics with Applications In the Management, Natural and Social Sciences (11th ed.). Boston, MA: Pearson.

ISBN-13: 9780321986320

COURSE STRUCTURE

Quantitative Business Analysis is a three-credit online course, consisting of

seven modules. Modules include learning objectives, study materials, activities, and quizzes. Module titles are listed below.

·

Module 1: Review of Basic Concepts

·

Module 2: Linear Equations and Inequalities

·

Module 3: Functions and Their Linear and Quadratic Applications

·

Module 4: Exponential and Logarithmic Equations

·

Module 5: Business and Finance Applications

·

Module 6: Systems and Matrices

·

Module 7: Maximization and Minimization

ASSESSMENT METHODS

For your formal work in the course, you are required to participate in online discussion forums, complete written assignments, take quizzes, and a proctored online final examination. See below for more details.

Consult the Course Calendar for assignment due dates.

Promoting Originality

One or more of your course activities may utilize a tool designed to promote original work and evaluate your submissions for plagiarism. More information about this tool is available in

this document

.

Discussion Forums

You will have seven discussion forum assignments in this course. One per module. You are required to enter an initial response to the Discussion Question. In addition, you must post at least two responses to the initial response of other students and these two responses must be on different days during the module. This standard is a minimum requirement. It is suggested that you participate on a daily basis during the course.

Participation consists primarily of discussion the topic under consideration or other topics of interest regarding mathematics and its business applications. Participation is measured by a student’s meaningful contribution to the virtual classroom discussion. Only substantive contributions will be considered for grading. Notes such as “me too” and “I agree” and other notes not related to the course are not considered substantive notes for participation. A note is determined to be of substance by containing information that supplements, contradicts, questions, or furthers discussion on a subject area contained in the course.

Submitting assignments through the Assignment links, logging on and reading messages, posting messages in the “Lounge” or in the “Introduction,” and emails do not count towards participation.

Participation grading will, by necessity, be a combination of objective grading (number of postings) and subjectivity (quality of postings).

Written Assignments

You are required to complete

seven written assignments. The written assignments are on a variety of topics associated with the course modules.

Assignments must be prepared electronically with a word processor (e.g., Microsoft Word) and, preferably, whatever equation editor integrates with your word processing software. Since this is a course in mathematics, you are recommended to use an equation editor to place mathematical symbols in your work. (

Important: Use the equation editor only to insert equations into your word-processed document and not to create the document itself.) However, if your word processor is not compatible with your mentor’s word processor, you will need to save your document as a rich-text format (.rtf) file before submitting it. Check with your mentor first to determine file compatibility.

When preparing your answers, please identify each exercise clearly by textbook section and exercise number. Be sure to include your name at the top of the paper, as well as the course name and code and the semester and year in which you are enrolled. To receive full credit for your answers, you must show all work and include complete solutions. If you choose not to use an equation editor to write mathematical symbols, you’ll need to use the

Insert > Symbols menu of your word processor to find the appropriate symbols. Exponents can be inserted as superscripts using the

Format > Font menu.

Quizzes

There will be a quiz for each of the seven modules. The quizzes should be taken after you complete the practice exercises and the written assignment. There will be

five multiple-choice problems on each of the quizzes. You have up to

30 minutes in which to complete the quiz and may take it

only once.

Final Exam

The proctored, online final exam covers all reading and assignments from the course. The exam is three hours long. The final exam includes 50 multiple choice questions.

You may use your textbook as long as it doesn’t have any loose inserts. You are not allowed to bring or consult a solutions manual, notebook or notes of any kind, any practice or written assignment problems, or any other reference sources or sources of information.

Note:

You are permitted to use a calculator (scientific, graphing, or financial) but

may not

use a calculator on a phone, PDA, or any similar device.

For the final, you are required to use the University’s

Online Proctor Service

(OPS). Please refer to the “Examinations and Proctors” section of the Online Student Handbook (see

Student Handbooks

in the General Information area of the course website) for further information about scheduling and taking online exams and for all exam policies and procedures. You are strongly advised to schedule your exam within the first week of the semester.

Online exams are administered through the course Web site. Consult the Course Calendar for the official dates of exam weeks.

Statement about Cheating

You are on your honor not to cheat during an exam. Cheating means:

· Looking up any answer or part of an answer in an unauthorized textbook or on the Internet, or using any other source to find an answer.

· Copying and pasting or, in any way copying responses or parts of responses from any other source into your exams. This includes but is not limited to copying and pasting from other documents or spreadsheets, whether written by yourself or anyone else.

· Plagiarizing answers.

· Asking anyone else to assist you by whatever means available while you take an exam.

· Copying any part of an exam to share with other students.

· Telling your mentor that you need another attempt at an exam because your connection to the Internet was interrupted when that is not true.

If there is evidence that you have cheated or plagiarized in an exam, the exam will be declared invalid, and you will fail the course.

GRADING AND EVALUATION

Your grade in the course will be determined as follows:

·

Discussion Forums—20 percent

·

Written Assignments—30 percent

·

Quizzes—20 percent

·

Final exam (proctored online, modules 1-7)—30 percent

All activities will receive a numerical grade of 0–100. You will receive a score of 0 for any work not submitted. Your final grade in the course will be a letter grade. Letter grade equivalents for numerical grades are as follows:

A

=

93–100

C+

=

78–79

A–

=

90–92

C

=

73–77

B+

=

88–89

C–

=

70–72

B

=

83–87

D

=

60–69

B–

=

80–82

F

=

Below 60

To receive credit for the course, you must earn a letter grade of C or better (for an area of study course) or D or better (for a course not in your area of study), based on the weighted average of all assigned course work (e.g., exams, assignments, discussion postings, etc.).

STRATEGIES FOR SUCCESS

First Steps to Success

To succeed in this course, take the following first steps:

· Read carefully the entire Syllabus, making sure that all aspects of the course are clear to you and that you have all the materials required for the course.

· Take the time to read the entire Online Student Handbook. The Handbook answers many questions about how to proceed through the course, how to schedule exams, and how to get the most from your educational experience at Thomas Edison State University.

· Arrange to take your examinations by following the instructions in this Syllabus and the Online Student Handbook.

· Familiarize yourself with the learning management systems environment—how to navigate it and what the various course areas contain. If you know what to expect as you navigate the course, you can better pace yourself and complete the work on time.

· If you are not familiar with Web-based learning be sure to review the processes for posting responses online and submitting assignments before class begins.

Study Tips

Consider the following study tips for success:

· To stay on track throughout the course, begin each week by consulting the Course Calendar. The calendar provides an overview of the course and indicates due dates for submitting assignments, posting discussions, and scheduling and taking examinations.

· Read the module objectives. The module learning objectives provide a roadmap of sorts for your studies. As you complete each module, check that you have covered and achieved all the objectives.

· Read the study notes, and follow the examples. Study notes review, highlight, and summarize key concepts, terms, and applications from the module assignment. They are written with classroom notes in mind, the type of notes you would take if you were in a face-to-face classroom environment. The language is easy to understand, and the notes include examples that show problem solving step by step.

· Remember, practice makes perfect. The textbook has odd-numbered exercises very similar to the even-numbered exercises in your assignments. Answers to odd-numbered exercises are at the back of the textbook (solutions are in the optional

Student’s Solution Manual). It is good practice to solve some of the odd-numbered exercises before working on the written assignments.

· Check Announcements regularly for new course information.

ACADEMIC POLICIES

To ensure success in all your academic endeavors and coursework at Thomas Edison State University, familiarize yourself with all administrative and academic policies including those related to academic integrity, course late submissions, course extensions, and grading policies.

For more, see:

·

University-wide policies

·

Undergraduate course policies and regulations

·

Graduate academic policies

·

Nursing student policies

·

Academic code of conduct

Copyright © 2016 by Thomas Edison State University. All rights reserved.

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Syllabus for MAT-121

COLLEGE ALGEBRA

WELCOME

Welcome to College Algebra! In this course, you will build skills that apply to a wide range of careers and personal interests. You will also join a community of adult learners who, with the guidance of a subject-matter expert, will exchange ideas, ask questions, and contribute to each other’s success. Whether your most recent math class was last semester or last millennium, you will find resources throughout the course that have been designed to support your learning. Take advantage of these opportunities to reinforce your understanding, close gaps in your knowledge, and challenge yourself to achieve more than you thought possible.

COURSE DESCRIPTION

This course builds upon the foundations of basic/intermediate algebra to further develop students’ mathematical knowledge and professional skill set. Students in a wide range of disciplines and careers build real-world technical skills through the use of technology, data, and application modeling. This course also emphasizes critical thinking, logic, problem solving, and analytical skills. Topics include a review of pre-algebraic concepts, linear equations and inequalities, quadratic equations, functions (linear, quadratic, polynomial, exponential, and logarithmic), real-world applications using modeling and applying regression analysis to data.

COURSE TOPICS

· Review of pre-algebraic concepts (prerequisites)

· Equations and inequalities

· Linear functions

· Polynomial and rational functions

· Exponential and logarithmic functions

COURSE OBJECTIVES

After completing this course, you should be able to:

CO 1 Apply critical thinking skills, problem solving skills, analyzing skills, and logic skills through the use of algebraic concepts and processes.

CO 2 Identify and use pre-algebraic and algebraic concepts.

CO 3 Use the Cartesian coordinate plane to graph equations and functions.

CO 4 Solve problems involving linear, quadratic, power, polynomial, rational, exponential, and logarithmic equations/functions.

CO 5 Model real-world applications involving linear functions, quadratic functions, rational functions, exponential functions, and logarithmic functions.

CO 6 Apply algebraic concepts and processes to model and solve real-world problems.

CO 7 Use scatter plots to analyze data through the use of curve fitting linear and exponential models.

CO 8 Solve problems involving linear and absolute value inequalities.

COURSE MATERIALS

You will need the following materials to complete your coursework. Some course materials may be free, open source, or available from other providers. You can access free or open-source materials by clicking the links provided below or in the module details documents. To purchase course materials, please visit the

University’s textbook supplier

.

Required Textbook

· Abramson, J. (2021).

College algebra. OpenStax.

·

Read the book online or download

Additional Learning Resources

·

CK-12 PLIX Interactive Algebraic Concepts

·

Wolfram Demonstrations

·

Desmos Graphing Tool

·

Geogebra Graphing Tool

·

Geogebra Classic Graphing Tool

·

Khan Academy

COURSE STRUCTURE

College Algebra is a three-credit online course consisting of

ten modules. Modules include an overview, topics, learning objectives, study materials, and activities. Module titles are listed below.

·

Module 1: Review of Pre-Algebraic Concepts, Part 1

Course objectives covered in this module: CO 1, CO 2

·

Module 2: Equations and Inequalities, Part 1

Course objectives covered in this module: CO 1, CO 2, CO 3, CO 4, CO 6

·

Module 3: Equations and Inequalities, Part 2

Course objectives covered in this module: CO 1, CO 2, CO 3, CO 4, CO 8

·

Module 4: Functions

Course objectives covered in this module: CO 1, CO 2, CO 3, CO 4

·

Module 5: Linear Functions

Course objectives covered in this module: CO 1, CO 2, CO 3, CO 4, CO 5, CO 6, CO 7

·

Module 6: Review of Pre-Algebraic Concepts, Part 2

Course objectives covered in this module: CO 1, CO 2, CO 4

·

Module 7: Polynomial and Rational Functions, Part 1

Course objectives covered in this module: CO 1, CO 2, CO 3, CO 4, CO 5

·

Module 8: Polynomial and Rational Functions, Part 2

Course objectives covered in this module: CO 1, CO 2, CO 4, CO 5

·

Module 9: Exponential and Logarithmic Functions, Part 1

Course objectives covered in this module: CO 1, CO 2, CO 3, CO 4, CO 6

·

Module 10: Exponential and Logarithmic Functions, Part 2

Course objectives covered in this module: CO 1, CO 2, CO 4, CO 5, CO 6, CO 7

ASSESSMENT METHODS

For your formal work in the course, you are required to participate in online discussion forums, complete practice exercises and technology activities, take quizzes, take a practice midterm and final examination, and take a proctored midterm and final examination. See below for details.

Consult the Course Calendar for due dates.

Promoting Originality

One or more of your course activities may utilize a tool designed to promote original work and evaluate your submissions for plagiarism. More information about this tool is available in

SafeAssign

.

Discussion Forums

You are required to complete

four discussion forums. The discussion forums are on a variety of topics associated with the course modules.

Communication with your mentor and classmates is a critical component of online learning. Participation in online class discussions involves two distinct activities: an initial response to a discussion question and at least two subsequent comments on classmates’ responses.

All of these responses must be substantial. Meaningful participation is relevant to the content, adds value, and advances the discussion. Comments such as “I agree” and “ditto” are not considered value-adding participation. Therefore, when you agree or disagree with a classmate or your mentor, state and support your position.

You will be evaluated on the quality and quantity of your participation, including your use of relevant course information to support your point of view, and your awareness of and responses to the postings of your classmates. Remember, these are discussions: responses and comments should be properly proofread and edited, mature, and respectful.

Refer to the

Evaluation Rubrics folder in the course website to view the Discussion Forum rubric for grading.

Practice Exercises

You are required to complete

ten practice exercises. For each assignment,

answer all assigned exercises, and show all work. Assignment sheets, with all questions typed out in advance for you, are provided for each assignment.

The preferred option for completing your practice exercises is to download the assignment sheet, complete and show all of your work in your downloaded file, and submit the completed file. Use a word processor and whatever equation editor integrates with your word processing software.

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

The alternate option is to complete your work by hand. This requires writing out and clearly labeling all exercises by number and textbook section, showing all work, scanning your completed document, and submitting your scanned file. All of your labeling and work

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Technology Activities

You are required to complete

five technology activities. The technology activities are on a variety of topics associated with the course modules. These activities will use Geogebra and Desmos online calculators to investigate specific content to obtain a deeper understanding of the algebraic concepts covered in each activity. Each activity has a template file that you will fill out electronically and submit along with the screenshots and/or copies of graphs and files created. There are instructional videos and examples to assist you in completing each activity.

Activities should be prepared electronically, using a word processor and whatever equation editor integrates with your word processing software. (Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.)

Note: Handwritten scanned documents are also allowed, provided that they are clearly legible.

Quizzes

You are required to take

eight quizzes. Quizzes are multiple choice, open book, untimed, and unproctored. A graphing calculator is provided as a tool within the quiz. Practice using this calculator, which will also be provided on your exams.

Each module quiz includes some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution videos that provide step-by-step explanations. Solution videos will be available the day after the quiz is due.

You are encouraged to take each quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

Think of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams.

Practice Exams

To reinforce your learning and help you feel confident about the exams, you will take

two required practice exams: a practice midterm exam and a practice final exam. They are located in the Examinations section of your course space. The practice exams’ questions were developed to closely resemble those on the actual exams.

The practice exams are required, unproctored, weighted activities, and you can take them multiple times (you’ll see the same questions each time). The score from your first attempt will be the only one recorded in the gradebook. The practice exams have 25 multiple-choice questions and a 3-hour time limit, just like the actual exams, and they provide the same calculator that is provided on all quizzes and exams. These required activities were created specifically to help you succeed on the midterm and final exams.

The practice exams provide feedback, so make note of any topics that you need to review. By using this feedback, referring to the Midterm Exam Study Guide and the Final Exam Study Guide, and reviewing the solution videos from selected quiz questions, you’ll know what to expect on the exams and can make sure you’re prepared for them.

Examinations

You are required to take

two proctored online examinations: a midterm exam and a final exam. In addition to the quiz solution videos and practice exams described above, exam study guides for the midterm and final exams are available in the Examinations section of the course space. The exam study guides provide details about the exams and comprehensive lists of the topics that will appear on the exams. Take advantage of all of these resources to ensure you are well prepared for your midterm and final exams.

Both exams require that you use the University’s

Online Proctor Service

(OPS). Please refer to the “Examinations and Proctors” section of the Online Student Handbook (see

Student Handbooks

in the General Information area of the course website) for further information about scheduling and taking online exams and for all exam policies and procedures. You are strongly advised to schedule your exam within the first week of the semester.

Online exams are administered through the course website. Consult the Course Calendar for the official dates of exam weeks.

Midterm Examination

· Course objectives covered by this exam include: CO 1 through CO 8

· Modules covered by this exam include: Modules 2 through 5

· Overview and purpose:

Proctored, online, closed book, 3-hour time limit

Final Examination

· Course objectives covered by this exam include: CO 1 through CO 7

· Modules covered by this exam include: Modules 7 through 10

· Overview and purpose:

Proctored, online, closed book, 3-hour time limit

Statement about Cheating

You are on your honor not to cheat during the exam. Cheating means:

· Looking up any answer or part of an answer in an unauthorized textbook or on the Internet, or using any other source to find the answer.

· Copying and pasting or in any way copying responses or parts of responses from any other source into your online test. This includes but is not limited to copying and pasting from other documents or spreadsheets, whether written by yourself or anyone else.

· Plagiarizing answers.

· Asking anyone else to assist you by whatever means available while you take the exam.

· Copying any part of the exam to share with other students.

· Telling your mentor that you need another attempt at the exam because your connection to the Internet was interrupted when that is not true.

If there is evidence that you have cheated or plagiarized in your exam, the exam will be declared invalid, and you will fail the course.

GRADING AND EVALUATION

Your grade in the course will be determined as follows:

·

Discussion forums

(4)—10%

·

Practice exercises (10)—30%

·

Practice exams (2)—2%

·

Technology activities (5)—15%

·

Quizzes

(8)—8%

·

Midterm exam (proctored, Modules 2–5)—15%

·

Final exam (proctored, Modules 7–10)—20%

All activities will receive a numerical grade of 0–100. You will receive a score of 0 for any work not submitted. Your final grade in the course will be a letter grade. Letter grade equivalents for numerical grades are as follows:

A

=

93–100

C+

=

78–79

A–

=

90–92

C

=

73–77

B+

=

88–89

C–

=

70–72

B

=

83–87

D

=

60–69

B–

=

80–82

F

=

Below 60

To receive credit for the course, you must earn a letter grade of C or better (for an area of study course) or D or better (for a course not in your area of study), based on the weighted average of all assigned course work (e.g., exams, assignments, discussion postings).

STRATEGIES FOR SUCCESS

First Steps to Success

To succeed in this course, take the following first steps:

· Read the entire Syllabus carefully, making sure that all aspects of the course are clear to you and that you have all the materials required for the course.

· Take time to read the entire Online Student Handbook. The Handbook answers many questions about how to proceed through the course, how to schedule exams, and how to get the most from your educational experience at Thomas Edison State University.

· Arrange to take your examination(s) by following the instructions in this Syllabus and the Online Student Handbook.

· Familiarize yourself with the learning management systems environment—how to navigate it and what the various course areas contain. If you know what to expect as you navigate the course, you can better pace yourself and complete the work on time.

· If you are not familiar with web-based learning, be sure to review the processes for posting responses online and submitting assignments before class begins.

Study Tips

Consider the following study tips for success:

· To stay on track throughout the course, begin each week by consulting the Course Calendar. The Course Calendar provides an overview of the course and indicates due dates for submitting assignments, posting discussions, and scheduling and taking examinations.

· Check Announcements regularly for new course information.

ACADEMIC POLICIES

To ensure success in all your academic endeavors and coursework at Thomas Edison State University, familiarize yourself with all administrative and academic policies including those related to academic integrity, course late submissions, course extensions, and grading policies.

For more, see:

·

University-wide policies

·

Undergraduate course policies and regulations

·

Graduate academic policies

·

Nursing student policies

·

Academic code of conduct

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121 • College Algebra

Final Exam Study Guide

©2022 Thomas Edison State University

All Rights Reserved

Exam Details

Modules assessed: 7–10

Materials allowed: graphing calculator

Duration: 3 hours

Exam Format

Multiple choice: 25 questions • apply concepts to solve problems

Correct answers are worth 4 points. Some “nearly correct” answers are worth 2 points.

Tips from the Test Development Team

·

How to Use the Study Guide to Help Prepare for Your Exam

·

How to Answer Multiple-Choice Questions

*Note: Use this study guide to prepare for your Practice Final Exam, which is a required activity, as well as your Final Exam. The questions on the practice exam closely resemble those on the actual exam. Also review the video solutions to selected quiz questions, which also closely resemble exam questions.

Module 7

· Rewriting Quadratics in Standard Form

· Polynomial Functions and Real-World Applications

· Writing Formulas for Polynomial Functions

· Graphing Polynomial Functions

· Identifying Zeros and Their Multiplicities

Module 8

· Synthetic Division

· Polynomial Division

· Remainder Theorem

· Factor Theorem

· Asymptotes and Intercepts of Rational Functions

· Writing Rational Functions

Module 9

· Compound Interest Formula

· Graphing Transformations of Exponential Functions

· Using Common Logarithms and Real-World Applications

· Converting from Exponential to Logarithmic Form

· Graphing Logarithmic Functions and Transformations

Module 10

· Logarithmic Properties

· Change-of-Base Formula

· Solving Logarithmic Equations

· Modeling Exponential Growth and Decay

· Using Newton’s Law of Cooling

· Using Logistic Growth Models

· Graphing Logarithmic Functions; Finding the Domain of a Logarithmic Function; Example 10 (Finding the Vertical Asymptote of a Logarithm Graph)

image2

calendar_22sep/calendar_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Course Calendar

The Course Calendar provides an overview of assignment due dates and when to begin each module. For details on each assignment, go to the course website and click the associated module.

Go to

Week-by-Week Dates

to see specific dates for the current semester.

SUMMARY OF ACTIVITIES AND ASSESSMENTS

Activity/Assessment

Week Due

Section in Which to Find Requirements

· Introductions Forum

· Discussion Forum 1

· Practice Exercises 1

1

Module 1

· Technology Activity 1

· Practice Exercises 2

· Module 2 Quiz

2

Module 2

· Technology Activity 2

· Practice Exercises 3

· Module 3 Quiz

3

Module 3

· Discussion Forum 2

· Practice Exercises 4

· Module 4 Quiz

4

Module 4

· Technology Activity 3

· Practice Exercises 5

· Module 5 Quiz

5

Module 5

· Discussion Forum 3

· Practice Exercises 6

6

Module 6

· Practice Midterm Exam

· Midterm Exam

7

Examinations

· Practice Exercises 7

· Module 7 Quiz

8

Module 7

· Technology Activity 4

· Discussion Forum 4

· Practice Exercises 8

· Module 8 Quiz

9

Module 8

· Practice Exercises 9

· Module 9 Quiz

10

Module 9

· Technology Activity 5

· Practice Exercises 10

· Module 10 Quiz

11

Module 10

· Practice Final Exam

· Final Exam

12

Examinations

WEEK-BY-WEEK CALENDAR

Week 1

· Monday—

BEGIN MODULE 1

· Tuesday—Introductions Forum: initial post due

· Wednesday—Discussion Forum 1: initial post due

· Thursday—Introductions Forum: comments due

· Friday—Discussion Forum 1: comments due

· Saturday—

· Sunday—Practice Exercises 1 due

Week 2

· Monday—

BEGIN MODULE 2

· Tuesday—

· Wednesday—

· Thursday—Technology Activity 1 due

· Friday—

· Saturday—Practice Exercises 2 due

· Sunday—Module 2 Quiz due

Week 3

· Monday—

BEGIN MODULE 3

· Tuesday—

· Wednesday—

· Thursday—Technology Activity 2 due

· Friday—

· Saturday—Practice Exercises 3 due

· Sunday—Module 3 Quiz

Week 4

· Monday—

BEGIN MODULE 4

· Tuesday—

· Wednesday—Discussion Forum 2: initial post due

· Thursday—

· Friday—Discussion Forum 2: comments due

· Saturday—Practice Exercises 4 due

· Sunday—Module 4 Quiz

Week 5

· Monday—

BEGIN MODULE 5

· Tuesday—

· Wednesday—

· Thursday—Technology Activity 3 due

· Friday—

· Saturday—Practice Exercises 5 due

· Sunday—Module 5 Quiz

Week 6

· Monday—

BEGIN MODULE 6

· Tuesday—

· Wednesday—Discussion Forum 3: initial post due

· Thursday—

· Friday—Discussion Forum 3: comments due

· Saturday—Practice Exercises 6 due

· Sunday—

Week 7

Midterm Exam Week: Take exam by Sunday of Week 7.

· Monday—

· Tuesday—

· Wednesday—Practice Midterm Exam due

· Thursday—

· Friday—

· Saturday—

· Sunday—Midterm Exam due

Week 8

· Monday—

BEGIN MODULE 7

· Tuesday—

· Wednesday—

· Thursday—

· Friday—

· Saturday—Practice Exercises 7 due

· Sunday—Module 7 Quiz

Week 9

· Monday—

BEGIN MODULE 8

· Tuesday—

· Wednesday—Technology Activity 4 due

· Thursday—Discussion Forum 4: initial post due

· Friday—

· Saturday—Discussion Forum 4: comments due; Practice Exercises 8 due

· Sunday—Module 8 Quiz

Week 10

· Monday—

BEGIN MODULE 9

· Tuesday—

· Wednesday—

· Thursday—

· Friday—

· Saturday—Practice Exercises 9 due

· Sunday—Module 9 Quiz

Week 11

· Monday—

BEGIN MODULE 10

· Tuesday—

· Wednesday—

· Thursday—Technology Activity 5 due

· Friday—

· Saturday—Practice Exercises 10 due

· Sunday—Module 10 Quiz due

Week 12

Final Exam Week: Take exam by Sunday of Week 12.

· Monday—

· Tuesday—

· Wednesday—Practice Final Exam due

· Thursday—

· Friday—

· Saturday—

· Sunday—Final Exam due

Copyright © 2022 by Thomas Edison State University. All rights reserved.

exam study guides_22sep/midterm exam study guide_MAT-121-sep22 x

MAT-121 • College Algebra

Midterm Exam Study Guide

©2022 Thomas Edison State University

All Rights Reserved

Exam Details

Modules assessed: 2–5

Materials allowed: graphing calculator

Duration: 3 hours

Exam Format

Multiple choice: 25 questions • apply concepts to solve problems

Correct answers are worth 4 points. Some “nearly correct” answers are worth 2 points.

Tips from the Test Development Team

·

How to Use the Study Guide to Help Prepare for Your Exam

·

How to Answer Multiple-Choice Questions

*Note: Use this study guide to prepare for your Practice Midterm Exam, which is a required activity, as well as your Midterm Exam. The questions on the practice exam closely resemble those on the actual exam. Also review the video solutions to selected quiz questions, which also closely resemble exam questions.

Module 2

· Finding a Linear Equation and Real-World Applications

· Using the Distance Formula and Real-World Applications

· Determining Whether Lines Are Parallel or Perpendicular

· Finding a Linear Equation and Models and Applications

· Using the Distance Formula and Models and Applications

Module 3

· Simplifying Powers of

i and Evaluating Complex Equations

· Solving Quadratic Equations by Factoring

· Solving Quadratic Equations by Using the Quadratic Formula

· Solving Inequalities

· Solving Absolute Value Inequalities

Module 4

· Finding Input and Output Values of a Function

· Function Notation

· Finding Domain and Range from Graphs and Using Notations to Specify Domain and Range

· Piecewise Defined Functions (Example 12, Working with a Piecewise Function)

· Average Rate of Change

· Local/Absolute, Minima/Maxima

· Composition of Functions and Real-World Application

Module 5

· Toolkit Functions and Transformations of Functions

· Function Transformations and Using Vertical and Horizontal Shifts

· Finding the Slope of a Line

· Parallel/Perpendicular Lines

· Linear Functions and Modeling with Linear Functions

· Linear Regression

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modules_22sep/module 7_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Module 7—Polynomial and Rational Functions, Part 1

OVERVIEW

Welcome to Module 7! This module expands upon the content covered in Module 6 by looking at all aspects of polynomial functions including quadratic and power functions: increasing/decreasing, extrema, zeros, and graphing. Polynomial functions have real-world applications in the volume of boxes, cylinders, and other forms of product containers.

TOPICS

Module 7 covers the following topics:

· Quadratic functions

· Power functions and polynomial functions

· Graphs of polynomial functions

OBJECTIVES

After successfully completing Module 7, you should be able to:

MO 7.1 Write quadratic equations in various forms (vertex, general, and standard). [CO 1, CO 2, CO 4]

MO 7.2 Solve real-world applications using the quadratic/polynomial function model. [CO 1, CO 2, CO 5]

MO 7.3 Identify power functions and their end behavior. [CO 1, CO 2, CO 4]

MO 7.4 Find the degree and leading coefficient of polynomial functions. [CO 1, CO 2, CO 4]

MO 7.5 Graph polynomial functions and identify all the significant features. [CO 1, CO 2, CO 3, CO 4]

MO 7.6 Write polynomial functions given a graph or information about a polynomial graph. [CO 1, CO 2, CO 4]

MO 7.7 Find the zeros and multiplicity of polynomial functions. [CO 1, CO 2, CO 4]

MO 7.8 Determine the minimum/maximum, domain/range, and axis of symmetry of polynomial functions. [CO 1, CO 2, CO 4]

STUDY MATERIALS

Textbook Readings

· Chapter 5, sections 5.1 through 5.3 in Abramson,

College Algebra

Additional Materials

· Khan Academy. (n.d.).

Solving quadratics by taking square roots

.

· Khan Academy. (n.d.).

Solving simple quadratics review

.

· Khan Academy. (n.d.).

Graph quadratics in vertex form

.

· Khan Academy. (n.d.).

Quadratic word problems (vertex form)

.

· CK-12. (n.d.).

Graph quadratic functions and equations: Soccer ball trajectory

. CK-12 PLIX Series.

· Pegg Jr., E. (2011, March 7).

End behavior of polynomial functions

. Wolfram Demonstrations Project.

· Zaborowski, E. (2011, March 7).

Polynomial graph generator

. Wolfram Demonstrations Project.

· Weisstein, E. (2007, April 27).

Cubic polynomial

. Wolfram Demonstrations Project.

·

Video Resources

Please note that these activities are not mandatory but should be utilized if you are struggling with any relevant content.

Self-Check Exercises

Work through the following practice exercises from the textbook. Then check your solutions with those in the

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 5.1: exercises 17, 27, 35, 43, 47, 51

·

Section 5.2: exercises 15, 23, 27, 35, 53, 61, 67

·

Section 5.3: exercises 15, 47, 49, 63, 71, 79

ACTIVITIES

Module 7 has two activities. Please consult the Course Calendar for the due dates.

Practice Exercises 7

As you start approaching the last modules of this course, you will continue to reinforce your skills by completing practice exercises. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 7.1 through MO 7.8]

Assignment sheet for Practice Exercises 7

A Note About Preparing Assignments

The preferred option for completing your practice exercises is to download the assignment sheet, complete and show all of your work in your downloaded file, and submit the completed file. Use a word processor and whatever equation editor integrates with your word processing software.

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

The alternate option is to complete your work by hand. This requires writing out and clearly labeling all exercises by number and textbook section, showing all work, scanning your completed document, and submitting your scanned file. All of your labeling and work

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 7 Quiz

Now that you are in the second half of the course, you know what to expect from module quizzes. The Module 7 quiz consists of multiple-choice problems focusing on what you’re learning in this module. The quiz is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams.

Keep in mind that each module quiz includes some problems that closely resemble problems that you’ll see on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

Keep thinking of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. [MO 7.1 through MO 7.6]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 2—Equations and Inequalities, Part 1

OVERVIEW

Welcome to Module 2! Now that we have reviewed pre-algebraic concepts, we are ready to build our foundation for solving and graphing equations. In this module you will learn about the Cartesian coordinate system (CCS) and graphing. The CCS has important practical applications including GPS systems, satellite technology, maps, and city planning and designing.

A highlight of this module is your first technology activity, in which you’ll investigate parallel and perpendicular lines using Geogebra, a free interactive math tool. The required practice exercises and formative quiz will also help you reinforce your knowledge and prepare for upcoming modules.

TOPICS

Module 2 covers the following topics:

· Cartesian coordinate system

· Intercepts

· Linear equations in one variable

· Rational equations

· Parallel and perpendicular lines

· Models and applications

OBJECTIVES

After successfully completing Module 2, you should be able to:

MO 2.1 Plot ordered pairs in a Cartesian coordinate system. [CO 1, CO 3]

MO 2.2 Graph equations by plotting points and finding the x and y intercepts. [CO 1, CO 3]

MO 2.3 Use the midpoint and distance formulas, given two points, and apply them to real-world applications. [CO 1, CO 2, CO 6]

MO 2.4 Solve various forms of linear equations in one variable. [CO 1, CO 2, CO 4]

MO 2.5 Determine if the graphs of the equations of two lines are perpendicular, parallel, or neither. [CO 1, CO 2, CO 4]

MO 2.6 Write the equation of a line parallel or perpendicular to a given line. [CO 1, CO 2, CO 4]

MO 2.7 Model and solve linear equations involving real-world applications. [CO 1, CO 2, CO 6]

STUDY MATERIALS

Textbook Readings

· Chapter 2, sections 2.1 through 2.3 in Abramson,

College Algebra

Additional Materials

· Khan Academy. (n.d.).

Intercepts of lines review (x-intercepts and y-intercepts)

.

· Hafner, I. (2014, May 1).

Solving a linear equation in one variable and two parameters

. Wolfram Demonstrations Project.

· CK-12. (n.d.).

Points in the coordinate plane

. CK-12 PLIX Series.

· CK-12. (n.d.).

Graphs of linear equations: Let’s play mini-golf

. CK-12 PLIX Series.

· CK-12. (n.d.).

Slope-intercept form of linear equations: Mountain train

. CK-12 PLIX Series.

·

Desmos. Lines: Slope Intercept Form

·

V

ideo Resources

Please note that these activities are not mandatory but should be utilized if you are struggling with any relevant content.

Self-Check Exercises

Work through the following practice exercises from the textbook. Then check your solutions with those in the

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 2.1: exercises 5, 11, 17, 23, 31, 35, 39, 49

·

Section 2.2: exercises 11, 21, 27, 33, 37, 41, 45

·

Section 2.3: exercises 7, 9, 17, 25, 47

ACTIVITIES

Module 2 has three activities. Please consult the Course Calendar for the due dates.

Technology Activity 1

During this course, you will complete several technology activities that are designed to require practical, hands-on application of the algebraic skills you are learning. You will develop technical skills to solve real-world problems and answer complex questions.

In this first technology activity, you will investigate parallel and perpendicular lines using technology. Parallel and perpendicular lines are very important mathematical concepts used in the designing and building of roads, home and building construction, map making, electrical circuit design and layout, clothing and textile manufacturing, and sports (just to name a few.) Using Geogebra, you will use the available features to create lines, determine the equations of each line, find slope, and create lines parallel to your created lines. Likewise, you will do a similar investigation using the perpendicular line feature in Geogebra. [MO 2.1, MO 2.2, MO 2.5, MO 2.6]

Technology Activity 1

Submit Technology Activity 1 and all your graph exports to your mentor for grading.

Practice Exercises 2

As you did in the last module, you will again complete practice exercises to help reinforce the skills you are learning. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 2.1 through MO 2.7]

Assignment sheet for Practice Exercises 2

A Note About Preparing Assignments

The preferred option for completing your practice exercises is to download the assignment sheet, complete and show all of your work in your downloaded file, and submit the completed file. Use a word processor and whatever equation editor integrates with your word processing software.

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

The alternate option is to complete your work by hand. This requires writing out and clearly labeling all exercises by number and textbook section, showing all work, scanning your completed document, and submitting your scanned file. All of your labeling and work

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 2 Quiz

Most modules in this course include a quiz. Think of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. You will be in excellent shape for your exams if you take your time on quizzes, pay close attention to the feedback you receive at the end, and use these tools to develop your skills.

In this module you will take your first quiz. Like every quiz in this course, it consists of multiple-choice problems focusing on what you’re learning in the module. The quiz is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams.

Each module quiz includes some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook. [MO 2.1 through MO 2.7]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 5—Linear Functions

OVERVIEW

Welcome to Module 5! We will be halfway through the course after completion of this module. This module looks specifically at linear functions. You will expand the concept of a function to linear equations. Linear functions will be graphed and modeled including real-world applications. The third technology activity is an introduction to linear function regression using real-world data collected by the SEER Program (cancer related data). The linear function created from this regression analysis can be used for modeling future trends in predicting cancer and helping with cancer research.

TOPICS

Module 5 covers the following topics:

· Linear functions

· Modeling with linear functions

· Fitting linear models to data

OBJECTIVES

After successfully completing Module 5, you should be able to:

MO 5.1 Identify and graph function transformation. [CO 1, CO 2, CO 3, CO 4]

MO 5.2 Determine if a function is odd, even, or neither. [CO 1, CO 2]

MO 5.3 Translate linear equations into linear functions. [CO 1, CO 2]

MO 5.4 Interpret slope as a rate of change. [CO 1, CO 2]

MO 5.5 Graph linear functions. [CO 1, CO 2, CO 3]

MO 5.6 Determine if two lines are parallel or perpendicular. [CO 1, CO 2]

MO 5.7 Write equations of parallel and perpendicular lines. [CO 1, CO 2, CO 4]

MO 5.8 Model linear functions from real-world applications. [CO 1, CO 2, CO 5, CO 6]

MO 5.9 Graph and interpret scatter plots; use a graphing utility to find the best line of fit

from real-world data. [CO 1, CO 2, CO 3, CO 6, CO 7]

STUDY MATERIALS

Textbook Readings

· Chapter 3, section 3.5 and Chapter 4, sections 4.1 through 4.3 in Abramson,

College Algebra

Additional Materials

· Hafner, I. (2011, March 7).

Linear function game

. Wolfram Demonstrations Project.

·

Video Resources

Please note that these activities are not mandatory but should be utilized if you are struggling with any relevant content.

Self-Check Exercises

Work through the following practice exercises from the textbook. Then check your solutions with those in the

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 3.5: exercises 9, 19, 25, 29, 35, 43, 49, 59, 67, 75

·

Section 4.1: exercises 11, 17, 25, 29, 39, 45, 49, 55, 61, 73, 87

·

Section 4.2: exercises 9, 25, 49, 55

·

Section 4.3: exercises 9, 19, 23, 39

ACTIVITIES

Module 5 has three activities. Please consult the Course Calendar for the due dates.

Technology Activity 3

Technology Activity 3 will expand your practical experience using the skills you are developing in this course.

In this activity, you will use real-world cancer research data from the SEER (Surveillance, Epidemiology, and End Results) program and technology for linear regression to find the best line of fit. The line found can be used to predict future trends in the specific cancer data you chose relating to the number of new cases and death rate (Geogebra graphing utility). [MO 5.4, MO 5.9]

Technology Activity 3

Submit Technology Activity 3 and all your graph exports to your mentor for grading.

Practice Exercises 5

You will complete practice exercises to help reinforce the skills you are learning in Module 5. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 5.1 through MO 5.9]

Assignment sheet for Practice Exercises 5

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 5 Quiz

The Module 5 quiz consists of multiple-choice problems focusing on what you’re learning in this module. The quiz is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams.

Keep in mind that each module quiz includes some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

As always, think of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. [MO 5.1, MO 5.3, MO 5.4, MO 5.6, MO 5.7, MO 5.8]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 8—Polynomial and Rational Functions, Part 2

OVERVIEW

Welcome to Module 8! This module expands upon the previous module on polynomial functions by finding the zeros of polynomials, applying long and synthetic division on polynomials, and applying the following theorems: rational root theorem, intermediate value theorem, Descartes’ rule of signs, and investigating end behavior. Rational expressions are expanded into rational functions with vertical and horizontal asymptotes, domain, and graphing. Real-world applications include volume and dimension for boxes, areas and length/width of rectangles, and dimensions of a right circular cone and cylinder.

TOPICS

Module 8 covers the following topics:

· Dividing polynomials

· Zeros of polynomial functions

· Rational functions

OBJECTIVES

After successfully completing Module 8, you should be able to:

MO 8.1 Divide polynomials using both long division and synthetic division. [CO 1, CO 2, CO 4]

MO 8.2 Evaluate a polynomial using the remainder theorem. [CO 1, CO 2, CO 4]

MO 8.3 Use the factor theorem, rational zero theorem, linear factorization theorem, and Decartes’ rule of signs to find the zeros of a polynomial. [CO 1, CO 2, CO 4]

MO 8.4 Solve real-world applications of polynomial and rational functions. [CO 1, CO 2, CO 4, CO 5]

MO 8.5 Identify vertical and horizontal asymptotes. [CO 1, CO 2, CO 4]

MO 8.6 Write rational functions with given characteristics. [CO 1, CO 2, CO 4]

MO 8.7 Graph rational functions. [CO 1, CO 2, CO 4]

STUDY MATERIALS

Textbook Readings

· Chapter 5, sections 5.4 through 5.6 in Abramson,

College Algebra

Additional Materials

· CK-12. (n.d.).

Long division of polynomials

. CK-12 PLIX Series.

· CK-12. (n.d.).

Oblique asymptotes: Rational functions and asymptotes

. CK-12 PLIX Series.

· CK-12. (n.d.).

Excluded values for rational expressions: Holes in rational functions

. CK-12 PLIX Series.

· CK-12. (n.d.).

Horizontal and vertical asymptotes: Rational functions

. CK-12 PLIX Series.

· Pegg, E., Jr. (2011, March 7).

Simple rational functions

. Wolfram Demonstrations Project.

· Bravo, E. (2011, March 7).

Synthetic division (Ruffini’s rule)

. Wolfram Demonstrations Project.

· Blake, S. (2011, March 7).

Polynomial long division

. Wolfram Demonstrations Project.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 5.4: exercises 5, 21, 47, 63, 67, 71

·

Section 5.5: exercises 7, 17, 27, 43, 59, 73, 79

·

Section 5.6: exercises 15, 29, 33, 37, 45, 53, 59, 75

ACTIVITIES

Module 8 has four activities. Please consult the Course Calendar for the due dates.

Technology Activity 4

This technology activity has many real-world applications. You will use Geogebra and Desmos to thoroughly investigate a fourth degree polynomial. Polynomials can be used in roller coaster rides to model curves and they can be used in road designs, buildings and other structures, polynomial regression for monthly prices of a commodity, and box design. Polynomials are also an essential tool in describing and predicting traffic patterns so appropriate traffic control measures, such as traffic lights, can be implemented. Using technology and the theorems of Chapter 5, you will determine the zeros, factor and graph the polynomial, locate all local extrema, and determine end behavior. [MO 8.1, MO 8.2, MO 8.3, MO 8.4]

Technology Activity 4

Submit Technology Activity 4 and all your graph exports to your mentor for grading.

Discussion Forum 4

In Discussion Forum 4, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Post your results from Technology Activity 4 and discuss what you investigated and how the technology helped you better understand all the aspects of a polynomial.

When replying to your classmates’ posts, compare your investigations and how the technology helped you better understand polynomials. Note any similarities and differences and add any suggestions you feel may be helpful in better understanding polynomials and if anything should be added/changed in the activity. This will not require much of your time and is more of an extension of Technology Activity 4. [MO 8.1, MO 8.2, MO 8.3, MO 8.4]

Practice Exercises 8

You have come a long way in this course. Keep doing your best with the practice exercises so you’ll finish strong. As always, this module’s exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 8.1 through MO 8.7]

Assignment sheet for Practice Exercises 8

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 8 Quiz

You are in the home stretch for this course’s quizzes. The Module 8 quiz, like all of the others, is multiple choice, open book, untimed, and unproctored. A graphing calculator is provided as a tool within the quiz. Practice using this calculator, which is also provided on your exams.

Keep thinking of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams.

As you know, some of the quiz problems closely resemble problems that you’ll see on your exam. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook. [MO 8.1 through MO 8.7]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 1—Review of Pre-Algebraic Concepts, Part 1

OVERVIEW

Welcome to College Algebra! This course will provide you with critical skills that have practical applications in business, science, healthcare, teaching, design, or any job that requires some degree of analytical thinking. College Algebra builds the necessary foundation for higher level mathematics such as precalculus and calculus. We will use technology like Geogebra and Desmos to enhance the understanding of the algebraic concepts covered throughout the course.

Module 1 consists of an introduction to successful study skills and a review of pre-algebraic concepts. Pre-algebra refers to the prerequisite arithmetic and geometry knowledge needed for algebra. Module 1 is part 1 of the review of pre-algebraic concepts; Module 6 is part 2. We will create a basic algebraic foundation that will be used for problem-solving throughout the course.

TOPICS

Module 1 covers the following topics:

· Study skills

· Real numbers

· Order of operations

· Algebraic expressions

· Exponents

· Scientific notation

· Radicals

· Rational exponents

OBJECTIVES

After successfully completing Module 1, you should be able to:

MO 1.1 Create a plan for improving mathematical study skills. [CO 1, CO 2]

MO 1.2 Classify a real number as natural, whole, integer, rational, or irrational. [CO 1, CO 2]

MO 1.3 Perform calculations on real numbers using order of operations and properties of real numbers. [CO 1, CO 2]

MO 1.4 Use the properties of exponents to simplify algebraic expressions. [CO 1, CO 2]

MO 1.5 Apply scientific notation to real-world applications. [CO 1, CO 2]

MO 1.6 Use the properties of radicals to simplify radical expressions. [CO 1, CO 2]

MO 1.7 Use the properties of rational exponents to simplify expressions. [CO 1, CO 2]

STUDY MATERIALS

Textbook Readings

· Chapter 1, sections 1.1 through 1.3 in Abramson,

College Algebra

Required Materials

·

Study Skills Survey

·

Plan for Improvement

Additional Materials

· CK-12. (2022, January 17).

Scientific notation

. CK-Foundation.

· CK-12. (n.d.).

Properties of exponents

. CK-Foundation.

· CK-12. (n.d.).

The real numbers: Number system

. CK-12 PLIX Series.

· CK-12. (n.d.).

Negative and zero exponents: Patterns with powers

. CK-12 PLIX Series.

· CK-12. (n.d.).

Multiplication and division of radicals: Totally radical dude’s height

. CK-12 PLIX Series.

· Bolte, J. (2011, March 7).

Scientific notation

. Wolfram Demonstrations Project.

· Nevell, J. (2011, November 16).

Integer exponents

. Wolfram Demonstrations Project.

· Beck, G. (2011, March 7).

Laws of exponents

. Wolfram Demonstrations Project.

· Khan Academy. (n.d.).

Radicals and rational exponents

.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 1.1: exercises 5, 7, 31, 39, 49, 53

·

Section 1.2: exercises 27, 39, 47, 49

·

Section 1.3: exercises 27, 31, 41, 57, 66

ACTIVITIES

Module 1 has three activities. Please consult the Course Calendar for the due dates.

Introductions Forum (Video Post)

As we start this course, let’s get to know each other a bit. Learning about each other will help us have more productive and engaging discussions throughout the semester.

Introduce yourself to your classmates and mentor in a video, and let us know the following:

· Your reasons for taking this course

· Your work experience and/or future career goals

· The last math class you took (state course name and year taken)

· How you’re feeling about taking this course (curious, confident, anxious, etc.)

Then, find an appropriate photograph or object that tells us something significant about yourself. Tell us about it and share why it’s important to you.

Reply with a written response to

at least two classmates’ video posts by the date indicated in the Course Calendar. In your replies, tell them if you have anything in common with them, or ask them questions about something they’ve shared that interests you. If you have insights or advice about something they’ve said, let them know.

Note: The Introductions Forum is not graded but is required.

For instructions on how to record and upload your video response, review the following document:

Using Video Tools in Moodle

.

Discussion Forum 1

In Discussion Forum 1, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Reflect on your past math experiences and create a plan for improvement. Download and fill out the two documents linked in the Required Materials section: Study Skills Survey and Plan for Improvement. Submit both completed documents to your mentor. Then, create a discussion forum thread where you share your completed Plan for Improvement document and also address the following questions:

· What was your score from the completed Study Skills Survey?

· Did your score surprise you? Why or why not?

· What challenges do you face, and what are some possible solutions?

Reply to

at least two posts by other students. In your replies, note whether you have any similar challenges as your classmates. Are there any challenges or possible solutions your classmates have that may assist your improvement plan? [MO 1.1]

Practice Exercises 1

In each module of this course, you will complete practice exercises to help reinforce the skills you are learning. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 1.2 through MO 1.7]

Assignment sheet for Practice Exercises 1

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 3—Equations and Inequalities, Part 2

OVERVIEW

Welcome to Module 3! This module is an introduction to complex numbers, which consist of real and imaginary numbers. Complex numbers have applications in advanced mathematics, physics, and engineering. This module also includes an introduction to quadratic equations and methods of solving quadratic equations. The graphs of quadratic equations can be seen all around us, such as the Gateway Arch in St. Louis and the symbol for McDonald’s. Inequalities are introduced with interval and set builder notation to represent their solution along with displaying solutions on a number line. The second technology activity covers an investigation into quadratic equations and inequalities using Geogebra and Desmos.

TOPICS

Module 3 covers the following topics:

· Complex numbers

· Quadratic equations

· Factoring

· Square root property

· Completing the square

· Quadratic formula and the discriminant

· Inequalities

OBJECTIVES

After successfully completing Module 3, you should be able to:

MO 3.1 Plot complex numbers in a Cartesian coordinate system. [CO 1, CO 3]

MO 3.2 Perform arithmetic operations on complex numbers and simplify powers of

i. [CO 1, CO 2, CO 4]

MO 3.3 Solve quadratic equations using various methods. [CO 1, CO 2, CO 4]

MO 3.4 Solve linear and absolute value inequalities using properties of inequalities and technology. [CO 1, CO 2, CO 8]

STUDY MATERIALS

Textbook Readings

· Chapter 2, sections 2.4, 2.5, and 2.7 in Abramson,

College Algebra

Additional Materials

· Khan Academy. (n.d.).

Intro to complex numbers

.

· Khan Academy. (n.d.).

Solving absolute value inequalities 1

[Video].

· Khan Academy. (n.d.).

Solving absolute value inequalities 2

[Video].

· Rivas, A. (2011, March 7).

Solution of quadratic equations

. Wolfram Demonstrations Project.

· Hafner, I. (2014, April 16).

Solving linear inequalities

. Wolfram Demonstrations Project.

· CK-12. (n.d.).

Inequality expressions: Inequality graph

. CK-12 PLIX Series.

· CK-12. (n.d.).

Multi-step inequalities: Summer camp

. CK-12 PLIX Series.

· Veera, C. (n.d.).

Graphing compound inequalities

on number

line

. GeoGebra.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 2.4: exercises 7, 11, 17, 33, 43, 55

·

Section 2.5: exercises 7, 23, 29, 37, 47, 53

·

Section 2.7: exercises 7, 13, 17, 23, 25, 29, 35, 45, 47, 51

ACTIVITIES

Module 3 has three activities. Please consult the Course Calendar for the due dates.

Technology Activity 2

As you know, this course requires several technology activities that are designed to provide practical, hands-on application of the algebraic skills you are learning. You will develop technical skills to solve real-world problems and answer complex questions.

For Technology Activity 2, you will use technology (a graphing calculator or online graphing utility like Desmos and Geogebra) to investigate quadratic equations and linear and absolute value inequalities. The graphs of quadratics are called parabolas and are used in the designs of parabolic objects like radio telescopes and satellite dishes. Inequalities are used in the manufacturing process of materials that must meet a certain tolerance in their specifications. This activity will help prepare you for professional tasks requiring knowledge of algebra. [MO 3.1 through MO 3.4]

Technology Activity 2

Submit Technology Activity 2 and all your graph exports to your mentor for grading.

Practice Exercises 3

By now you are getting accustomed to practice exercises. This module’s exercises, like those in every module, will help reinforce the skills you are learning. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 3.1 through MO 3.4]

Assignment sheet for Practice Exercises 3

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 3 Quiz

The Module 3 quiz consists of multiple-choice problems focusing on what you’re learning in this module. The quiz is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams.

Each module quiz includes some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

Remember to think of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. [MO 3.3, MO 3.4]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 10—Exponential and Logarithmic Functions, Part 2

OVERVIEW

Welcome to the final module! It’s time to explore logarithmic properties and their close relationship to exponential properties. You’ll utilize these properties to solve real-world exponential and logarithmic models like Newton’s law of cooling, exponential growth of viruses, and the logistic growth model. For the last technology activity, you will use Desmos and exponential regression to fit a model to real-world radioactive isotope data.

TOPICS

Module 10 covers the following topics:

· Logarithmic properties

· Change-of-base formula

· Exponential and logarithmic equations

· Exponential and logarithmic models

· Newton’s law of cooling

· Logistic-growth model

· Fitting exponential models to data

OBJECTIVES

After successfully completing Module 10, you should be able to:

MO 10.1 Apply logarithmic properties. [CO 1, CO 2, CO 4]

MO 10.2 Solve exponential and logarithmic equations. [CO 1, CO 2, CO 4, CO 5, CO 6]

MO 10.3 Solve applied problems using exponential and logarithmic equations. [CO 1, CO 2, CO 4, CO 5, CO 6]

MO 10.4 Model exponential growth and decay. [CO 1, CO 2, CO 4, CO 5]

MO 10.5 Use Newton’s law of cooling to solve real-world problems. [CO 1, CO 2, CO 6]

MO 10.6 Model exponential data using regression. [CO 1, CO 2, CO 5 CO 7]

MO 10.7 Use the logistic growth model to solve problems. [CO 1, CO 2, CO 5, CO 7]

MO 10.8 Apply change-of-base formula. [CO 1, CO 2, CO 5, CO 7]

MO 10.9 Find the domain, vertical asymptotes, and end behavior for logarithmic functions. [CO 1, CO 2, CO 5, CO 7]

STUDY MATERIALS

Textbook Readings

· Chapter 6, sections 6.5 through 6.8 in Abramson,

College Algebra

Additional Materials

· Khan Academy. (n.d.).

Solve exponential equations using exponent properties

.

· Khan Academy. (n.d.).

Interpret change in exponential models

.

· Khan Academy. (n.d.).

Construct exponential models

.

· Khan Academy. (n.d.).

Intro to logarithm properties

.

· Khan Academy. (n.d.).

Justifying the logarithm properties

.

· Khan Academy. (n.d.).

Logarithm change of base rule intro

.

· Khan Academy. (n.d.).

What are the logarithm properties?

· Khan Academy. (n.d.).

Solving exponential equations using logarithms

.

· Khan Academy. (n.d.).

Exponential model word problems

.

· CK-12. (n.d.).

Logarithm properties: The log properties

. CK-12 PLIX Series.

· Rivas, A. (2011, March 7).

Calculating integer logarithms in different bases

. Wolfram Demonstrations Project.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 6.5: exercises 11, 19, 23, 31, 33

·

Section 6.6: exercises 5, 26, 35, 37, 47, 55, 71, 77

·

Section 6.7: exercises 7, 15, 21, 33, 43, 52

·

Section 6.8: exercises 31, 32, 33, 41, 42, 43

ACTIVITIES

Module 10 has three activities. Please consult the Course Calendar for the due dates.

Technology Activity 5

In your last technology activity of the course, you will use Desmos and exponential regression to model real-world radioactive isotope data. A tool in Desmos, called a

slider, will be used to manipulate the decay rate to model your equation as close as possible to your data. [MO 10.6]

Technology Activity 5

Submit Technology Activity 5 and all your graph exports to your mentor for grading.

Practice Exercises 10

You have made it to the last set of practice exercises! As you have been doing all along, you’ll reinforce this module’s skills by completing practice exercises that are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 10.1 through MO 10.9]

Assignment sheet for Practice Exercises 10

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 10 Quiz

The Module 10 quiz is the last quiz in this course! Like all of the previous quizzes, it is multiple choice, open book, untimed, and unproctored. A graphing calculator is provided as a tool within the quiz. Practice using this calculator, which is also provided on your exams.

Each module quiz includes some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

Remember to think of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. [MO 10.1, MO 10.2, MO 10.3, MO 10.4, MO 10.5, MO 10.6]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 6—Review of Pre-Algebraic Concepts, Part 2

OVERVIEW

Welcome to Module 6! In this module you will continue your review of pre-algebraic concepts that began in Module 1. The module covers polynomials, factoring polynomials, and rational expressions and is the foundation for Module 7 on polynomial and rational functions. You will also take a survey of exam study skills and create a plan for success when taking mathematics exams. The survey and plan can then be utilized throughout your educational career.

TOPICS

Module 6 covers the following topics:

· Polynomials

· Factoring polynomials

· Rational expressions

OBJECTIVES

After successfully completing Module 6, you should be able to:

MO 6.1 Formulate a plan for mathematics exam success. [CO 1]

MO 6.2 Classify and identify the degree of polynomials. [CO 1, CO 2, CO 4]

MO 6.3 Perform basic operations on polynomials. [CO 1, CO 2, CO 4]

MO 6.4 Factor polynomials using various techniques. [CO 1, CO 2, CO 4]

MO 6.5 Perform basic operations to simplify rational expressions. [CO 1, CO 2, CO 4]

MO 6.6 Simplify complex rational expressions. [CO 1, CO 2, CO 4]

STUDY MATERIALS

Textbook Readings

· Chapter 1, sections 1.4 through 1.6 in Abramson,

College Algebra

Required Materials

·

P

lan for Success

·

Mathematics Exam Study Skills Survey

Additional Materials

· Khan Academy. (n.d.).

Adding and subtracting polynomials review

.

· Khan Academy. (n.d.).

Multiplying monomials by polynomials review

.

· Khan Academy. (n.d.).

Multiplying binomials by polynomials review

.

· Khan Academy. (n.d.).

Intro to rational expressions

.

· CK-12. (n.d.).

Polynomials in standard form

. CK-12 PLIX Series.

· CK-12. (n.d.).

Addition and subtraction of polynomials: Splitting into tiles

. CK-12 PLIX Series.

· CK-12. (n.d.).

Multiply polynomials by binomials: Rainbows

. CK-12 PLIX Series.

· CK-12. (n.d.).

Special products of polynomials: Difference of two squares

. CK-12 PLIX Series.

· CK-12. (n.d.).

Factor quadratics: Algebra tiles

. CK-12 PLIX Series.

· CK-12. (n.d.).

Factor by grouping: Polynomials

. CK-12 PLIX Series.

· CK-12. (n.d.).

Multiplication of rational expressions

. CK-12 PLIX Series.

· CK-12. (n.d.).

Division of rational expressions: Step by step

. CK-12 PLIX Series.

· Nochella, J. (2011, March 7).

Squaring a binomial

. Wolfram Demonstrations Project.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 1.4: exercises 17, 27, 35, 43, 47, 51

·

Section 1.5: exercises 15, 23, 27, 35, 53, 61, 67

·

Section 1.6: exercises 15, 47, 49, 63, 71, 79

ACTIVITIES

Module 6 has two activities. Please consult the Course Calendar for the due dates.

Discussion Forum 3

In Discussion Forum 3, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Reflect on your past experiences in taking math exams and create a plan for success using a growth mindset. Download and fill out the two documents linked in the Required Materials section: Mathematics Exam Study Skills Survey and Plan for Success. Submit both completed documents to your mentor. Then, create a discussion forum thread where you share your completed Plan for Success document and address the following questions:

· What was your score from the completed Mathematics Exam Study Skills Survey?

· Did your score surprise you? Why or why not?

· What challenges do you face, and what are some possible solutions?

Reply to

at least two posts by other students. In your replies, note whether you have any similar challenges as your classmates. Are there any challenges or possible solutions your classmates have that may assist your improvement plan? [MO 6.1]

Practice Exercises 6

As you have been doing in each module, you will complete practice exercises to help reinforce the skills you are learning. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 6.1 through MO 6.6]

Assignment sheet for Practice Exercises 6

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 9—Exponential and Logarithmic Functions, Part 1

OVERVIEW

Welcome to Module 9, coming down the home stretch! This module explores exponential and logarithmic functions and the relationship between the two; graphing exponential and logarithmic functions and their transformations; and solving real-world applications involving exponential and logarithmic functions like the intensity of earthquakes, compound interest, investments, virus/bacteria exponential growth, and isotope decay.

TOPICS

Module 9 covers the following topics:

· Exponential functions

· Graphs of exponential functions

· Logarithmic functions

· Graphs of logarithmic functions

OBJECTIVES

After successfully completing Module 9, you should be able to:

MO 9.1 Find the equation of exponential functions. [CO 1, CO 2, CO 4]

MO 9.2 Use compound interest formulas. [CO 1, CO 2, CO 4, CO 6]

MO 9.3 Graph exponential functions and their transformations. [CO 1, CO 2, CO 3]

MO 9.4 Convert exponential form to logarithmic form and vice versa. [CO 1, CO 2, CO 4]

MO 9.5 Evaluate logarithms. [CO 1, CO 2, CO 4]

MO 9.6 Use common and natural logarithms to solve real-world applications. [CO 1, CO 2, CO 4]

MO 9.7 Graph logarithmic functions and their transformations and determine the domain. [CO 1, CO 2, CO 3]

STUDY MATERIALS

Textbook Readings

· Chapter 6, sections 6.1 through 6.4 in Abramson,

College Algebra

Additional Materials

· Khan Academy. (n.d.).

Intro to logarithms

.

· Khan Academy. (n.d.).

Evaluate logarithms

.

· Khan Academy. (n.d.).

Relationship between exponentials and logarithms

.

· Khan Academy. (n.d.).

e

and compound interest

[Video].

· Khan Academy. (n.d.).

Graphs of exponential functions

.

· Khan Academy. (n.d.).

Graphs of logarithmic functions

.

· CK-12. (n.d.).

Solving equations with exponents: Exponent interest model

. CK-12 PLIX Series.

· Beck, G. (2011, March 7).

Laws of exponents

. Wolfram Demonstrations Project.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 6.1: exercises 7, 9, 15, 21, 29, 47, 53, 61, 65

·

Section 6.2: exercises 11, 25, 27, 37, 43, 47

·

Section 6.3: exercises 9, 43, 53, 65

·

Section 6.4: exercises 17, 35, 45, 49, 53

ACTIVITIES

Module 9 has two activities. Please consult the Course Calendar for the due dates.

Practice Exercises 9

Almost there! As you have been doing in each module, you will complete practice exercises to help reinforce the skills you are learning. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 9.1 through MO 9.7]

Assignment sheet for Practice Exercises 9

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 9 Quiz

It is time for your second-to-last module quiz. Keep in mind that these are meant to be skill-building activities. They provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

Each module quiz, including this one, has some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due.

Now is also a good time to get a head start on your exam prep by reading the Final Exam Study Guide, located in the Assessments section of your course space. It lists all of the topics and skills you’ll need for the exam. If anything on it is unfamiliar as you study for the exam, be sure to review your textbook, re-watch the quiz solution videos, or speak with your mentor.

The quiz consists of multiple-choice problems focusing on what you’re learning in the module. It is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams. [MO 9.1 through MO 9.7]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 4—Functions

OVERVIEW

Welcome to Module 4! This module is an introduction to one of the most powerful concepts in mathematics, the function. Functions are used extensively in higher mathematics (calculus), physics, and engineering. They are also used in real-world technologies including vending machines, ATMs, self-serve car washes, change machines in laundromats, and automatic IV machines (a liquid/medicine is dripped into a patient’s vein at a constant rate). You will learn the characteristics of a function, as well as graphing and modeling linear functions including real-world applications.

TOPICS

Module 4 covers the following topics:

· Functions and function notation

· Vertical line test

· Domain and range

· Rates of change

· Behavior of graphs

· Composite functions

· Transformations

OBJECTIVES

After successfully completing Module 4, you should be able to:

MO 4.1 Determine if a relation represents a function utilizing various techniques (definition and the vertical line test). [CO 1, CO 2, CO 3]

MO 4.2 Determine if a function is one-to-one. [CO 1, CO 2, CO 3]

MO 4.3 Evaluate functions for given values of a variable. [CO 1, CO 2, CO 4]

MO 4.4 Write relations and equations in function notation. [CO 1, CO 2, CO 4]

MO 4.5 Graph a variety of functions. [CO 1, CO 2, CO 3]

MO 4.6 Find the range and domain of a function. [CO 1, CO 2]

MO 4.7 Find the average rate of change (slope) of a function. [CO 1, CO 2]

MO 4.8 Use a graph to determine if the function is increasing or decreasing and locate any extrema. [CO 1, CO 2, CO 3]

MO 4.9 Determine the composition of two or more functions and find its domain. [CO 1, CO 2, CO 4]

STUDY MATERIALS

Textbook Readings

· Chapter 3, sections 3.1 through 3.4 in Abramson,

College Algebra

Additional Materials

· CK-12. (2016, February 18).

Functions

. CK-12 Foundation.

· CK-12. (n.d.).

Identify functions and the vertical line test: Vertical line test

. CK-12 PLIX Series.

· CK-12. (n.d.).

Composition of functions: Composite functions

. CK-12 PLIX Series.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 3.1: exercises 9, 29, 41, 53, 57, 61, 63, 71, 81, 89

·

Section 3.2: exercises 9, 29, 41, 49, 53

·

Section 3.3: exercises 7, 17, 19, 27, 31, 39, 45

·

Section 3.4: exercises 5, 13, 19, 27, 43, 57, 67, 73, 91

ACTIVITIES

Module 4 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 2

In Discussion Forum 2, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Using either a stairway or a handicap access ramp (specific data values given), model a linear function and determine if the stairs/ramp are “up to code” based on International Building Codes (stairs) or ADA ramp requirements. [MO 4.3, MO 4.4, MO 4.6]

Option 1—Stairs

Measure the rise and run of several steps and calculate the equation of the line of the stairs.

Option 2—Ramp

Choose one from each set and post the values to the forum. You must choose a pair of values not already selected by a classmate.

Height list: 24.5, 25, 25.5, 26, 26.5, 27, 27.5, 28, 28.5, 29, 29.5

Slope ratio: 1:12, 1:12.5, 1:13, 1:13.5, 1:14, 1:14.5, 1:15

Practice Exercises 4

You are nearing the halfway point of this course. To help reinforce the skills you are learning in Module 4, you will complete practice exercises based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 4.1 through MO 4.9]

Assignment sheet for Practice Exercises 4

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 4 Quiz

By now you are getting used to taking module quizzes. Keep in mind that these are meant to be skill-building activities. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

Each module quiz, including this one, has some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due.

Looking ahead, now is also a good time to start reading the Midterm Exam Study Guide located in the Assessments section of your course space. It lists all of the topics and skills you’ll need for the exam. If anything on it is unfamiliar as you prepare for the exam, be sure to review your textbook, re-watch the quiz solution videos, or speak with your mentor.

Like every quiz in this course, this one consists of multiple-choice problems focusing on what you’re learning in the module. The quiz is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams. [MO 4.3, MO 4.4, MO 4.5, MO 4.6, MO 4.7]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Technology Activity 4—Polynomial List

Pick a problem from the list below. Post a message to the discussion forum indicating which problem you have chosen so that other members will know to select other problems.

1.

2.

3.

4.

5.

6.

7.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

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MAT-121: COLLEGE ALGEBRA

Technology Activity 2—Quadratic Equation List

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

hint: convert to common denominator with

18.

hint: convert to common denominator with

19.

hint: convert to common denominator with

20.

hint: convert to common denominator with

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MAT-121: COLLEGE ALGEBRA

Technology Activity 1—Investigation of Parallel and Perpendicular Lines

This technology activity will utilize the graphing and solving capabilities of

Geogebra’s Classic graphing utility

. When you open Geogebra, you may be prompted to select graphing from the menu on the right. For help using Geogebra and the tools, check out the

instructional video

.

Parallel Lines with Positive Slope

For help with this portion of the activity, check out the

instructional video

and accompanying

example

.

Parallel lines have the same slope and different

y-intercepts. Lines that are parallel to each other will never intersect.

Step 1: Using the

point

tool, place two points in the coordinate plane. These two points should be labeled

A and

B. (Make sure the coordinates of the ordered pairs are integer values, which will make the calculations easier.)

Make sure the two points will create a line with positive slope. Write down the two ordered pairs.

A: ____________ B:______________

Step 2: Click the

line

tool and select

Line. Then click on the two points, beginning with

A, in the coordinate plane. Make sure to click exactly on each point so your equation that is displayed has integer values. Write the equation given in Geogebra (should be in standard form).

Standard form: ___________________

Step 3: Click the

angle

tool

and select

Slope. Click on point

A to obtain the slope of the line. (Note: Your slope may be given as a decimal value.)

Slope:_______________________

Step 4: Rewrite the equation given in standard form in Geogebra into slope-intercept form. Also, write the slope in non-decimal form (i.e., as a fraction representing rate of change).

Show all the algebra steps.

Slope-intercept form: __________________________

Non-decimal slope: _________

Step 5: Click on the space to the right of the + sign (

Input) and enter an equation for a line with the same slope, but a different

y-intercept from the first equation. Your lines should be parallel. Write the equation you entered below.

Slope-intercept form: _______________________

Step 6: To verify your lines are parallel, use the

Slope tool to verify the slopes are the same.

Step 7: Save your graph by clicking on the menu button in the top right

and select

Export Image, then

Download.

Step 8: Click on the circles to the left of the second equation and its slope to hide them from the coordinate plane. The circles should have no color at all (white background).

Step 9: Another way to create parallel lines in Geogebra is to utilize the

Parallel Line tool. Click the

Perpendicular Line

icon and select

Parallel Line. Click on your line and drag your mouse, exposing the parallel line, and place it so it will have the same

y-intercept that you have/had in the second equation, which had been hidden. (Note: If your line is slightly off then you can click on its ordered pair coordinates and enter the values for the

y-intercept. Press the ENTER key on your computer. This should automatically adjust your line’s equation to the correct values). Use the

Slope

tool to verify the slope of the second line is the same as the first line.

Step 10: Write the equation of the line (standard form) given in Geogebra.

Standard form: ____________________________

Step 11: Rewrite the above equation in slope-intercept form

showing all algebra steps. Verify your equation matches.

Slope-intercept form: ____________________________

Step 12: Save your graph by clicking on the menu button in the top right and select

Export Image, then

Download. Make sure your exported images have different names. You may want to name it something to do with the positive slope of parallel lines because we are about to repeat the same process, but starting with two points that will give us a

negative slope.

Parallel Lines with Negative Slope

Step 13: Click on the

menu icon and then

+ New option to create a new graph.

Step 14: Using the

point tool, place two points on the coordinate plane. These two points should be labeled

A and

B. (Make sure the coordinates of the ordered pairs are integer values, which will make the calculations easier.)

Make sure the two points will create a line with negative slope. Write down the two ordered pairs.

A: ______________ B:______________

Step 15: Click the

line icon and select

Line. Then click on the two points, beginning with

A, in the coordinate plane. Make sure to click exactly on each point so your equation that is displayed has integer values. Write the equation given in Geogebra (should be in standard form).

Standard form: _______________________

Step 16: Click the

angle icon

and select

Slope. Click on point

A to obtain the slope of the line. Note: Your slope may be given as a decimal value.

Slope:_______________________

Step 17: Rewrite the equation given in standard form in Geogebra into slope-intercept form. Also, write the slope in non-decimal form (i.e., as a fraction representing rate of change).

Show all the algebra steps.

Slope-intercept form: __________________________

Non-decimal slope: _________

Step 18: Enter a new equation for a parallel line with a different

y-intercept from the first equation. Your lines should be parallel. Enter your equation below.

Slope-intercept form: ____________________

Step 19: To verify your lines are parallel, use the

Slope tool to ensure the slopes are the same. Save your graph by clicking on the menu button in the top right and select

Export Image, then

Download.

Step 20: Click on the circles to the left of the second equation and its slope to hide them from the coordinate plane. The circles should have no color at all (white background).

Step 21: Click the

Perpendicular Line icon and select

Parallel Line. Click on your line and drag your mouse, exposing the parallel line, and place it so it will have the same

y-intercept that you have/had in the second equation, which had been hidden. Use the

Slope

tool to verify the slope of the second line is the same as the first line.

Step 22: Write the equation of the line (standard form) given in Geogebra.

Standard form: ____________________________

Step 23: Rewrite the above equation in slope-intercept form

showing all algebra steps. Verify your equation matches.

Slope-intercept form: ____________________________

Step 24: Export the image to be uploaded at the end of the activity with all the other uploads. You may want to name it something to do with the negative slope of parallel lines.

Perpendicular Lines

For help with this portion of the activity, check out the

instructional video

.

Perpendicular lines have slopes that are negative reciprocals of each other. You can also show that two lines are perpendicular if the product of the two slopes is -1.

Step 25: Click on the circles to the left of the second equation and its slope to hide them from the coordinate plane. The circles should have no color at all (white background).

Step 26: Using the slope of your first line, create an equation that is perpendicular to the given line (first line in Geogebra). Enter that equation below and then into Geogebra.

Perpendicular line: _____________________________

Step 27: Verify that the slopes are negative reciprocals by using the

Slope tool on the perpendicular line. Export the image so that it can be submitted with the activity.

Step 28: Click on the circles for the items of the perpendicular line and slope. (Make sure you click on the

Arrow/Move icon before clicking on the circles or another slope will appear after the line has been removed from the coordinate plane.)

Step 29: Another way to create perpendicular lines in Geogebra is to utilize the

Perpendicular Line tool. Click on the

Perpendicular line icon

and

select the

Perpendicular Line. Click on the given line to create a perpendicular line. Move the perpendicular line so that it passes through the origin.

Step 30: Use the

Slope icon tool on the perpendicular line to verify that the slopes of the two lines are negative reciprocals of each other.

Step 31: Write down the given equation in standard form then rewrite the given equation in

slope-intercept form.

Make sure to show all the algebra.

Standard form:

_________________________

Slope-intercept form: ________________________

Step 32: Export the image to be uploaded with submission of this document. You may want to name it something to do with the perpendicular lines.

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MAT-121: COLLEGE ALGEBRA

Technology Activity 3

You are now going to investigate linear regression using

Geogebra classic

.

For help with this activity, check out the

instructional video

and accompanying

example

.

Select a data set from

this folder

. Post a message to the discussion forum indicating which data set you have chosen so that your classmates will know to select other sets. (

Note:

Data sets are selected on a first-come basis. If a classmate has already chosen a data set you had wanted to use, please select a different one.)

Data Set Name: _______________________________

Step 1: Set the axes values based on our data set. Click on the

Tools icon in the upper right area of the grid.

You should see the following screen. Click on the

settings icon.

You can now set the

x and

y axes values based on our data set values. Since you are mapping 1975 to

t = 0 and the last year, 2018, to

t = 43, you will have our

x values go from -5 as the “x Min” value and to 50 for our “x Max” value. This is the same for any data set chosen. Your

y values will be determined by your data values in the columns

New Cases and

Death Rates.

Note: If you use the Heart Disease data, you will use the “Number of Deaths—Male” as your

New Cases (1st scatter plot) data and the “Number of Deaths—Female” as your

Death Rates (2nd scatter plot) data. For “y Min” set it to a value of -5, and for “y Max” set it to 5 more than the largest value in either one of these columns.

Step 2: After you have set your values, click on the X to close out

Tools. Click on the

Input area to the left and start entering your ordered pairs for

New Cases.

The point will be displayed in the grid and Geogebra will move down to the next

Input line for your next ordered pair.

After you have entered all your data points you should have a scatter plot that looks something like the following. (Note: If your data set values decrease you will have a scatter plot with a negative slope.)

Step 3: You will now visually select your best line of fit. Make sure the

Point icon is selected. Click to the lower left (or upper left) of your scatter plot at where you think the best line of fit should start. Geogebra will place a point there, label it the next letter in line and place its ordered pair values below the last point you manually entered.

Step 4: Change the color of this point so that you know it is the one you selected for your visual best line of fit. To do this right click on the point in the grid. The following screen will be displayed. You want to click on

Settings.

The settings are displayed on the right. Click on the

Color tab and select a color different from the one in the scatter plot.

After you have made your choice, click the X to close out the settings window.

Step 5: Click on the

Line tool icon and select

Line.

Next click on your point you entered visually and adjust your line to what you think the best fit should be. (This should be based on trying to have as many points on your line or as close as possible.)

Finish the line by clicking again. Geogebra will display the equation of your line in the

Input area on the left below your visual point. Above the equation of the line is the second point based on where you clicked to complete your line. You can change the color of this point to match the other one.

You will now make the line the same color as your two points. Right click on the line, select

Settings and then

Color and select the same color as the points. Close out the settings window.

Step 6: Enter the equation from your visual best line of fit below.

Standard form: _____________________________________

Enter the algebra steps to rewrite your equation above in

y-intercept form.

Y-intercept form: _____________________________________

Step 7: You are now ready to have Geogebra determine your best line of fit. Click on the

Perpendicular Line tool icon and select

Best Fit Line.

Select the region you want Geogebra to determine the best fit line. Click in the upper left corner or your scatter plot and drag your mouse down to include the lower right area.

After you have selected your region, lift your finger off the left mouse button and the line will appear in your grid along with its equation to the left.

Your lines won’t exactly match up, but there will probably be an area in the middle where the lines cross as shown above.

Step 8: Enter the best fit line Geogebra determined.

Y-intercept form: _________________________________

Step 9: Compare your visual best line of fit to Geogebra’s best line of fit. Give a brief discussion on how close the estimates were.

Step 10: Estimate the range of

x values where the two lines intersect and have the same values, stated in interval format.

x-values: ____________________

Save your graph by clicking on the menu button in the top right

and select

Export Image, then

Download.

Now, you will find the best line of fit using the

Death Rates column data. Repeat Steps 1 through 10 and fill in the information below.

Step 11: Enter the equation from your visual best line of fit below:

Standard form: _____________________________________

Enter the algebra steps to rewrite your equation above in

y-intercept form.

Y-intercept form: _____________________________________

Step 12: Enter the best fit line Geogebra determined below:

Y-intercept form: _________________________________

Step 13: Compare your visual best line of fit to Geogebra’s best line of fit. Give a brief discussion on how close the estimates were.

Step 14: Estimate the range of

x values where the two lines intersect and have the same values, stated in interval format.

x-values: ____________________

Save your graph by clicking on the menu button in the top right

and select

Export Image, then

Download.

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technology activities_22sep/technology activity 5_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Technology Activity 5

We are now going to investigate exponential regression using

Desmos calculator

.

For help with this activity, check out the

instructional video

and accompanying

example

.

Select an isotope and accompanying data set from

the list

. Post a message to the discussion forum indicating which isotope you have chosen so that your classmates will know to select other isotopes. (

Note:

Isotopes are selected on a first-come basis. If a classmate has already chosen an isotope you had wanted to use, please select a different one.) Enter the name of your isotope below.

Isotope name: _______________________________

The first thing you are going to do is adjust your

x and

y axes so you can view all the points in your data set. To set the

x and

y ranges click on the

Graph Settings icon.

All isotope

y values will range from -25 to 1050 with a step of 100. The

x values will range from -1000, -100 or -10, it all depends on your smallest

x value. If your smallest

x value (besides 0) is between 1 and 10 then use -10; if the smallest

x value is in between 10 and 100 use -100; if the smallest

x value is in between 100 and 1000 then use -500; if the smallest value is in between 1000 and 10,000 then use -1000. Likewise, for the largest

x value use 10, 100, 1000, or 10,000 more than the largest

x value. The step should also be based on the values of

x for your isotope. You can also add labels to the

x and

y axes based on the time (years or days) and “Amount” for the

y axis.

Now add your data set into a table in Desmos. In the input 1 line, type in

table. Desmos will start the table.

Enter your data into the table. Do not enter the last value where the amount remaining is close to zero.

Adjust the view of the graph by clicking the

Zoom Out icon on the right side (see the figure below). Zoom out until all your data points are displayed in the grid. Don’t worry about having the last point or two being displayed, especially if their values are so much greater than the other values.

Now enter an exponential expression in the input 2 line based on the initial value of your data set. All the isotopes have an initial value/amount of 1000, so enter . Desmos will ask you to create a slider for

r. Click on “

add slider

r”.

Clicking on the button will create the slider.

Adjust your slider values so that you can determine the best exponential fit for your data. Small increments of

r makes it easier to adjust the graph accordingly.

The slider values for your isotope were given in the table of isotopes. Values given will be the slider minimum, maximum, and the step.

You edit the color of your points by clicking on the circle to the left of

y and holding the mouse button down until the edit box comes up. Select the color you want and then press the ENTER key.

Adjust the slider so it covers most of your data points.

Enter your final regression equation here: y =

Save your graph by clicking

in the upper right corner and select

Export Image, then

Download.

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technology activities_22sep/technology activity 5 isotope data_MAT-121-sep22 x

The left column of the data table contains the time it took to decay to the amount given in the second column. The half-life of the isotope is given before the slider values. Use the given slider values in Desmos when you create your slider to determine the regression equation. The last entry in column 1 for any isotope should not be entered into Desmos since it will skew your data and make it difficult to view the other data points. The value is given so you know how long it takes for the isotope to completely decay.

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Barium (Ba) 133

0

1000

1.945

900

4.014

800

5.846

700

7.038

600

11.045

500

14.380

400

18.938

300

25.781

200

36.172

100

375.729

0.000000005 ≈ 0

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Bismuth (Bi) 207

0

1000

6.231

900

12.993

800

21.054

700

27.995

600

40.813

500

52.238

400

64.635

300

85.023

200

128.912

100

1,465.259

0.000000005 ≈ 0

Days to Decay to Remaining Amount

Amount Remaining

slider ranges:

Cerium (Ce) 144

0

1000

40.169

900

95.428

800

140.139

700

219.298

600

279

500

384.428

400

480.298

300

699.428

200

1006.428

100

10,001.703

0.000000005 ≈ 0

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Cesium (Cs) 137

0

1000

3.586

900

10.126

800

13.525

700

25.234

600

33.17

500

36.883

400

48.404

300

76.053

200

112.223

100

1,212.618

0.000000005 ≈ 0

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Krypton (Kr) 85

0

1000

2.029

900

4.451

800

7.516

700

9.900

600

12.72

500

15.171

400

20.620

300

26.891

200

34.611

100

412.442

0.000000005 ≈ 0

Days to Decay to Remaining Amount

Amount Remaining

slider ranges:

Polonium (Po) 210

0

1000

19.976

900

46.426

800

74.011

700

98.701

600

135

500

189.426

400

255.701

300

304.426

200

479.426

100

5,580.687

0.000000005 ≈ 0

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Plutonium (Pu) 238

0

1000

10.338

900

31.249

800

43.154

700

66.669

600

82.75

500

120.999

400

146.419

300

210.749

200

301.499

100

3,254.241

0.000000005 ≈ 0

This isotope, Plutonium 239, is only here as a reference to go along with the instructional video and not available to be selected for your activity.

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Plutonium (Pu) 239

0

1000

3603.275

900

7818.467

800

12511.213

700

17060.871

600

25105.233

500

32158.467

400

41160.871

300

57358.467

200

83258.467

100

924,743.138

0.000000005 ≈ 0

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Plutonium (Pu) 240

0

1000

965.020

900

2312.533

800

3,404.726

700

4,580.276

600

6,903.492

500

8,702.533

400

11,090.276

300

16,062.533

200

22,032.533

100

240,817.859

0.000000005 ≈ 0

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Radium (Ra)226

0

1000

238.205

900

525.085

800

841.317

700

1,209.145

600

1,665.876

500

2,205.085

400

2,709.145

300

3,845.085

200

5,395.085

100

60,875.934

0.000000005 ≈ 0

Days to Decay to Remaining Amount

Amount Remaining

slider ranges:

Ruthenium (Ru) 106

0

1000

54.785

900

121.148

800

183.848

700

279.466

600

401.541

500

479.148

400

651.466

300

878.148

200

1,189.148

100

13,987.624

0.000000005 ≈ 0

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Thorium (Th)229

0

1000

1,105.703

900

2,412.952

800

3,826.967

700

5,369.327

600

7,147.834

500

10,002.952

400

12,249.327

300

17,842.952

200

24,882.952

100

277,052.474

0.000000005 ≈ 0

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Thorium (Th) 230

0

1000

11,824.238

900

25,008.463

800

39,032.134

700

57,446.351

600

78,819.833

500

101,548.463

400

135,146.351

300

175,438.463

200

261,028.463

100

2,780,673.096

0.000000005 ≈ 0

Days to Decay to Remaining Amount

Amount Remaining

slider ranges:

Manganese (Mn) 54

0

1000

46.577

900

102.763

800

166.061

700

225.670

600

318.573

500

422.763

400

539.670

300

742.763

200

1,109.763

100

12,357.398

0.000000005 ≈ 0

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Niobium (Nb)b94

0

1000

3,030.062

900

6,448.562

800

10,191.463

700

14,639.312

600

22,913.581

500

25,538.562

400

35,239.312

300

45,738.562

200

67,038.562

100

755,914.181

0.000000005 ≈ 0

Years to Decay to Remaining Amount

Amount Remaining

slider ranges:

Actinium (Ac) 227

0

1000

3.909

900

7.468

800

12.202

700

15.044

600

23.77

500

27.078

400

39.214

300

51.948

200

70.998

100

822.772

0.000000005 ≈ 0

Days to Decay to Remaining Amount

Amount Remaining

slider ranges:

Antimony (Sb) 124

0

1000

9.951

900

21.080

800

33.577

700

43.865

600

62.920

500

80.580

400

109.565

300

143.780

200

190.980

100

2,301.981

0.000000005 ≈ 0

Days to Decay to Remaining Amount

Amount Remaining

slider ranges:

Gadolinium 153

0

1000

35.785

900

79.907

800

121.527

700

181.346

600

249

500

312.907

400

443.346

300

550.907

200

845.907

100

9244.973

0.000000005 ≈ 0

Days to Decay to Remaining Amount

Amount Remaining

slider ranges:

Cobalt (Co) 57

0

1000

40.041

900

89.921

800

144.935

700

193.981

600

269.582

500

363.921

400

498.981

300

581.921

200

930.921

100

10,306.126

0.000000005 ≈ 0

technology activities_22sep/technology activity 4_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Technology Activity 4

Given . Let a0 and an be nonzero. Then each rational solution x can be written in the form for p and q satisfying two properties:

1. p is an integer factor of a0, and

2. q is an integer factor of the coefficient an.

Select a polynomial from

this list

. Post a message to the discussion forum indicating which polynomial you have chosen so that your classmates will know to select other sets. (

Note:

Polynomials are selected on a first-come basis. If a classmate has already chosen a polynomial you had wanted to use, please select a different one.)

1.

Enter your polynomial here:

Use the LCD of the fractions to make your polynomial contain only whole numbers

Polynomial without fractions:

Use

Geogebra

to graph your polynomial.

a. Possible values of p:__________________________________________________

b. Possible values of q:__________________________________________________

c. Possible values of :_________________________________________________

d. Values of for which the function value is zero:____________________________

e. Zero(s) from the graph:______________________

f. Considering both the table of values and the graph, zeros or roots are identified by…

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

g. Rational roots of:___________________________________

h. Does the graph show any zeros that are complex? Explain how you determined this.

_____________________________________________________________________

_____________________________________________________________________

i. How do you distinguish the complex zeros from the rational real zeros for a given polynomial?

_____________________________________________________________________

_____________________________________________________________________

Synthetic Division Using Rational Zeros

Using your two zeros above, you will perform synthetic division to divide your 4th degree polynomial to a 3rd degree polynomial and then a quadratic polynomial. This will allow you to factor or use the quadratic formula to find the complex zeros/roots.

j. State the quadratic polynomial: __________________________

k. Identify any complex zeros for the polynomial:_____________________________

l. Why does it make sense that complex roots exist as conjugate pairs? (Hint: Which theorem states this?)

_____________________________________________________________________

_____________________________________________________________________

Save your graph by clicking on the menu button in the top right

and select

Export Image, then

Download.

Descartes’ Rule of Signs

Descartes’ Rule of Signs tells us of a relationship between the number of sign changes in and the number of positive real zeros.

Given any polynomial,

f(x),

1. Write it with the terms in descending order, i.e. from the highest degree term to the lowest degree term, .

2. Count the number of sign changes of the terms in

f(x). Call the number of sign changes

n.

3. Then the number of

positive roots of

f(x) is less than or equal to

n.

4. Further, the possible number of positive roots is

n,n−2,n−4,…

For example, if there are 3 sign changes then there would be 3 or 1 (3-2) positive real roots. If there are 4 sign changes then there would be 4, 2, or 0 positive real roots.

For place the signs of each term here (do not forgot the sign of the first term):

State the number of sign changes:

State the number of possible positive real roots using the above information:

There is a similar relationship between the number of sign changes in

p(-x) and the number of negative real zeros.

Note: If the exponent (degree) of a term is odd then

-x will yield a negative value. For example, if our term was , then since 2 negatives multiplied together make a positive. For even exponents (degree) then the term will be the sign in front of the coefficient. For example, .

For place the signs of each term here (do not forgot the sign of the first term):

State the number of sign changes:

State the number of possible negative real rootS using the above information:

Let’s verify your special points by using Geogebra. Bring up

Geogebra Classic

.

For help with this activity, check out the

instructional video

and accompanying

example

.

Enter your polynomial in the first input box.

You may have to click on the

Zoom Out icon to see the complete graph.

Click on the three vertical dots to the right of your polynomial and select

Special Points.

Verify that the roots and extrema you found in your original graph (the visually selected extrema in the first portion) are the same as the ones found here.

State the 4 special points from Geogebra:

and select

Export Image, then

Download.

Create a table of positive/negative values on each side of a real root/zero to determine if the graph is above/below the root/zero. You can also use your graph in Desmos to determine this:

Interval

Test Point

Value of

f(

x)

Sign of

f(

x)

Graph above or below

x-axis

Determine end behavior of the polynomial

Using your graph in Desmos, state what

f(x) approaches as

x approaches -∞:

Using your graph in Desmos, state what

f(x) approaches as

x approaches ∞:

State the

y-intercept (in ordered pair format):

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practice exercises_22sep/practice exercises 10_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Practice Exercises 10

SECTION 6.5

Algebraic

For the following exercise, condense to a single logarithm if possible.

1. .

For the following exercise, use the properties of logarithms to expand the logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs.

2.

For the following exercise, condense the expression to a single logarithm using the properties of logarithms.

3.

Numeric

For the following exercise, use properties of logarithms to evaluate without using a calculator.

4.

For the following exercise, use the change-of-base formula to evaluate the expression as a quotient of natural logs. Use a calculator to approximate each to five decimal places.

5.

SECTION 6.6

Algebraic

For the following exercise, use like bases to solve the exponential equation.

6. .

For the following exercise, use logarithms to solve.

7. .

For the following exercise, use the definition of a logarithm to solve the equation.

8. .

For the following exercise, use the one-to-one property of logarithms to solve.

9.

For the following exercise, solve the equation for

x.

10. .

Graphical

For the following exercise, solve the equation for x if there is a solution. Then graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution.

11. .

Technology

For the following exercise, solve the equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places.

12. using the common log.

For the following exercise, use a calculator to solve the equation. Round the answer to the nearest ten-thousandth.

13. Atmospheric pressure in pounds per square inch is represented by the formula , where

x is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of pounds per square inch? (Hint: There are 5280 feet in a mile.)

SECTION 6.7

Numeric

For the following exercise, use the logistic growth model

14. Find and interpret . Round to the nearest tenth.

Technology

For the following exercise, enter the data from the table into a graphing calculator and graph the resulting scatter plot. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.

15.

x

f(x)

1.25

5.75

2.25

8.75

3.56

12.68

4.2

14.6

5.65

18.95

6.75

22.25

7.25

23.75

8.6

27.8

9.25

29.75

10.5

33.5

For the following exercise, use a graphing calculator and this scenario: The population of a fish farm in years is modeled by the equation

16. To the nearest whole number, what will the fish population be after 2 years?

Real-World Applications

For the following exercise, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day.

17. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days. Round to the nearest tenth of a gram.

For the following exercise, use this scenario: A pot of warm soup with an internal temperature of 100͑° Fahrenheit was taken off the stove to cool in a 69°F room. After fifteen minutes, the internal temperature of the soup was 95°F.

18. Use Newton’s Law of Cooling to write a formula that models this situation.

For the following exercise, use this scenario: The equation models the number of people in a town who have heard a rumor after t days.

19. As increases without bound, what value does

N(t) approach? Interpret your answer.

SECTION 6.8

x

1

2

3

4

5

6

f(x)

1125

1495

2310

3294

4650

6361

20. Use a graphing calculator/utility to create a scatter diagram of the data. Use the regression feature to find an exponential function that best fits the data in the table. Write the exponential function as an exponential equation with base .

x

1

2

3

4

5

6

f(x)

5.1

6.3

7.3

7.7

8.1

8.6

21. Use the LOGarithm option of the REGression feature to find a logarithmic function of the form that best fits the data in the table. Use the logarithmic function to find the value of the function when .

This work, “Practice Exercises 10,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 10” is licensed under CC BY 4.0 by Thomas Edison State University.

practice exercises_22sep/practice exercises 1_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Practice Exercises 1

SECTION 1.1

For the following exercises, simplify the given expression.

1.

2.

For the following exercise, evaluate the expression using the given variable.

3. for

a = -2

For the following exercises, simplify the expression.

4.

5.

For the following exercise, consider this scenario: Fred earns $40 at the community garden. He spends $10 on a streaming subscription, puts half of what is left in a savings account, and gets another $5 for walking his neighbor’s dog.

6. How much money does Fred keep? Show all the work.

SECTION 1.2

For the following exercise, express the number in scientific notation.

7. The average distance between Earth and the Sun is 92,960,000 mi.

For the following exercise, convert the number in scientific notation to standard notation.

8. To reach escape velocity, a rocket must travel at the rate of ft/min.

For the following exercises, simplify the given expression. Write answers with positive exponents.

9.

10.

SECTION 1.3

For the following exercises, simplify each expression.

11.

12.

For the following exercises, simplify each expression.

13.

14.

Real-World Application

15. A plane accelerates at a rate of where

t is the time in seconds after the plane moves from rest. Simplify the expression.

This work, “Practice Exercises 1,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 1” is licensed under CC BY 4.0 by Thomas Edison State University.

technology activities_22sep/technology activity 2_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Technology Activity 2—Investigation of Quadratic Equations and Linear and Absolute Value Inequalities

This technology activity will utilize the graphing and solving capabilities of

Geogebra’s Classic graphing utility

and

Desmos graphing calculator

.

For help using Geogebra and the tools, check out the

instructional video

.

For help using Desmos and the tools, check out the

instructional video

.

Quadratics Equations

For help with this portion of the activity, check out the

instructional video

and accompanying

example

.

Step 1: We will now investigate quadratic equations using Geogebra. Select an

equation from the list

. Post a message to the discussion forum indicating which equation you have chosen so that your classmates will know to select other problems. (

Note:

Equations are selected on a first-come basis. If a classmate has already chosen an equation you had wanted to use, please select a different equation.) Click on the space to the right of the + sign (

Input) and enter your selected quadratic equation. If all of the graph is not displayed in the grid, use the zoom out icon until all of the graph is displayed in the grid. We have entered . For help entering quadratics and other special functions, check out

this video

.

Step 2: Solve your quadratic equation using either factoring, completing the square, or the quadratic formula. Place your solutions below. These “solutions” are also known as

x-intercepts, and zeros (since they make the

y coordinate of the

x-intercept equal to 0.)

Show your algebra work here:

Solution 1: ________________________ Solution 2: ____________________

Step 3: With your quadratic equation in general form , we can use the coefficients of the squared term and the linear term to find the coordinates of the vertex. To find the

x coordinate of the vertex use this formula: . To find the

y coordinate of the vertex just plug the preceding

x value into the quadratic equation. Write the coordinates of the vertex and the

y-intercept below.

General form: _________________________

a: ___________ b: _________

Vertex: _________________

Y-intercept: _________________

Step 4: Now we will use the tools in Geogebra to verify our results from Steps 2 and 3. Click the three vertical dots to the right of your quadratic equation and select

Special Points.

Step 5: Verify the values in Geogebra are the same as the ones above. Note that

Root represents the

x-intercepts,

Extremum represents the vertex, and

Intersect represents the

y-intercept. Write the values below.

Roots: ____________ and _______________

Extremum: _________________

Intersect: _____________

Step 6: Save your graph by clicking on the menu button in the top right

and select

Export Image, then

Download. For the last investigation of this activity we will be using Desmos.

Linear Inequalities

For help with this portion of the activity, check out the

instructional video

.

Navigate to the Desmos calculator by clicking on the following link:

Desmos calculator

. To get additional help using Desmos click on the question mark icon in the upper right corner.

Step 7: Click on the

tools icon

and uncheck the

Y-axis so you deal with just a number line (though our inequalities will be shaded).

Step 8: You will be investigating four inequalities:

1.

2.

3.

4.

Enter the first inequality in the top box. Since Desmos (and most online graphing utilities) are 2-D (two-dimensional) and inequalities will show up shaded and we will need to properly interpret them when we graph them on our number line. If the area is shaded to the left with a dotted vertical line then the solution is < (less than); shaded to the left with a solid vertical line then the solution is ≤ (less than or equal to); shaded to the right with a dotted vertical line then the solution is > (greater than); shaded to the right with a solid vertical line then the solution is ≥ (greater than or equal to).

Note: For the less than or equal to and the greater than or equal to inequalities you will need to type them in as <= and >= and Desmos will change them to respectively.

Step 9: Write the solution to your first inequality below. Then, write the original inequality and show the algebra to find the solution. Verify that your algebraic solution is the same as the one you just found in Desmos. Then graph your solution on the number line provided below.

Inequality #1:

Solution (write in both interval and set builder notation): ___________________

Original inequality: ______________________

Algebraic steps for solution:

Graphed solution:

Step 10: Click on the circle to the left of your inequality to remove it from the grid without removing your inequality. Repeat the above process for your other three inequalities.

Inequality #2:

Solution (write in both interval and set builder notation): ___________________

Original inequality: ______________________

Algebraic steps for solution:

Graphed solution:

Inequality #3:

Solution (write in both interval and set builder notation): ___________________

Original inequality: ______________________

Algebraic steps for solution:

Graphed solution:

Inequality #4:

Solution (write in both interval and set builder notation): ___________________

Original inequality: ______________________

Algebraic steps for solution:

Graphed solution:

Step 11: Save your graph by clicking

in the upper right corner and select

Export Image then

Download.

Absolute Value Inequalities

Absolute value

inequalities will give solutions very similar to compound inequalities. There will either be a shaded region between two values (representing an AND compound inequality) or two separate shaded regions (representing an OR compound inequality).

Step 12: Start with a new blank graph in Desmos. Click on the three horizontal bars in the upper left (Open Graph) and then click on New Blank Graph.

Step 13: Similar to compound inequalities, absolute value inequalities will be shaded and you will need to properly interpret them when you graph them on your number line. See the posted example for this activity to get more precise information on solving absolute value inequalities.

Step 14: You will be investigating four absolute value inequalities:

1.

2.

3.

4.

Enter the first absolute value inequality in the top box. You will get a shaded region(s) representing the two solutions.

Step 15: Write the solution to your first absolute value inequality below. Then, write the original absolute value inequality and show the algebra to find the solution. Verify that your algebraic solution is the same as the one you just found in Desmos. Then graph your solution on the number line provided below.

Absolute value inequality #1:

Solution (write in both interval and set builder notation): ___________________

Original absolute value inequality: ______________________

Algebraic steps for solution:

Graphed solution:

Step 16: Click on the circle to the left of your inequality to remove it from the grid without removing your inequality. Repeat the above process for your other three inequalities.

Absolute value inequality #2:

Solution (write in both interval and set builder notation): ___________________

Original absolute value inequality: ______________________

Algebraic steps for solution:

Graphed solution:

Absolute value inequality #3:

Solution (write in both interval and set builder notation): ___________________

Original absolute value inequality: ______________________

Algebraic steps for solution:

Graphed solution:

Absolute value inequality #4:

Solution (write in both interval and set builder notation): ___________________

Original absolute value inequality: ______________________

Algebraic steps for solution:

Graphed solution:

Step 17: Save your graph by clicking

in the upper right corner and select

Export Image, then

Download.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 3

SECTION 2.4

For the following exercise, evaluate the algebraic expression.

1. If , evaluate

y given .

Graphical

For the following exercise, plot the complex numbers on the complex plane.

.

2.

Numeric

For the following exercises, perform the indicated operation and express the result as a simplified complex number.

3.

4.

Technology

For the following exercise, use a calculator to help answer the question.

5. Evaluate for . Predict the value if

Extensions

For the following exercise, evaluate the expression, writing the result as a simplified complex number.

6.

SECTION 2.5

For the following exercise, solve the quadratic equation by factoring

7.

For the following exercise, solve the quadratic equation by using the square root property.

8.

For the following exercise, solve the quadratic equation by completing the square. Show each step.

9.

For the following exercise, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve.

10.

Technology

For the following exercise, enter the expressions into your graphing utility and find the zeros to the equation (the x-intercepts) by using 2nd CALC 2:zero. Recall finding zeros will ask left bound (move your cursor to the left of the zero, enter), then right bound (move your cursor to the right of the zero, enter), then guess (move your cursor between the bounds near the zero, enter). Round your answers to the nearest thousandth.

If you are using the

Desmos calculator

, then enter the first equation and press the ENTER key on your keyboard to get to #2. Enter the 2nd equation. The graphed quadratic and horizontal line will appear in the coordinate plane. You will see two dots representing the two points of intersection. Place your cursor over the dots representing the two solutions (points of intersection) and write down the order pairs.

11. To solve the quadratic equation we can graph these two equations

and and find the points of intersection. Recall 2nd CALC 5:intersection. If you are using the Desmos calculator, then refer to the steps above. Do this and find the solutions to the nearest tenth.

Extensions

12. Abercrombie and Fitch stock had a price given as , where the time in months is from 1999 to 2001 ( is January 1999). Find the two months in which the price of the stock was $30.

SECTION 2.7

Algebraic

For the following exercises, solve the inequality or absolute value inequality. Write your final answer in interval notation.

13.

14.

15.

16.

For the following exercise, describe all the x-values within or including a distance of the given values.

17. Distance of 10 units from the number 4.

For the following exercise, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation.

18.

Graphical

For the following exercise, graph the function. Observe the point of intersection and shade the x-axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.

19.

Numeric

For the following exercise, write the set in interval notation.

20.

For the following exercise, write the interval in set-builder notation.

21.

For the following exercise, write the set of numbers represented on the number line in interval notation.

22.

This work, “Practice Exercises 3,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 3” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 7

SECTION 5

.1

Algebraic

For the following exercise, rewrite the quadratic function in standard form and give the vertex. Determine whether there is a minimum or maximum value to the quadratic function. Find

the value and the axis of symmetry. Determine the domain and range.

1.

For the following exercise, use the vertex and a point on the graph to find the general form of the equation of the quadratic function.

2.

Graphical

For the following exercise, sketch a graph of the quadratic function and give the vertex, axis of symmetry, and intercept.

3.

For the following exercise, write the equation for the graphed quadratic function.

4.

Numeric

For the following exercise, use the table of values that represent points on the graph of a quadratic function. By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.

5.

x

-2

-1

0

1

2

y

8

2

0

2

8

Technology

For the following exercise, use a calculator or graphing utility to find the answer.

6. Graph on the same set of axes

.

What appears to be the effect of adding a constant?

SECTION 5.2

Algebraic

For the following exercise, identify the function as a power function, a polynomial function, or neither. If the function is polynomial then find the degree and leading coefficient for the given polynomial.

7.

For the following exercise, determine the end behavior of the function and find the intercepts of the function.

8.

Graphical

For the following exercise, determine the least possible degree of the polynomial function shown.

9.

Technology

For the following exercise, graph the polynomial function using a calculator or graphing utility. Based on the graph, determine the intercepts and the end behavior.

10.

Extensions

For the following exercise, use the information about the graph of a polynomial function to determine the function. Assume the leading coefficient is 1 or –1. There may be more than one correct answer.

11. The

y-intercept is (0,9). The

x-intercepts are (-3,0), (3,0). Degree is 2.

Real-World Applications

For the following exercise, use the written statements to construct a polynomial function that represents the required information.

12. An oil slick is expanding as a circle. The radius of the circle is increasing at the rate of 20 meters per day. Express the area of the circle as a function of the number of days elapsed. The area of a circle is and the diameter is twice the radius.

SECTION 5.3

Algebraic

For the following exercise, find the or t-intercepts of the polynomial functions.

13.

Graphical

For the following exercises, graph the polynomial functions. Note

y-intercept, all zeros and their multiplicity, and end behavior.

14.

For the following exercise, use the graph to write the formula for a polynomial function of least degree. Identify zeros and their multiplicity.

15.

For the following exercise, use the given information about the polynomial graph to write the equation.

16. Degree 3. Zeros at .

y-intercept at .

Technology

For the following exercise, use a calculator to approximate local minima and maxima or the global minimum and maximum.

17.

Real-World Applications

For the following exercise, write the polynomial function that models the given situation.

18. A cylinder has a radius of units and a height of 3 units greater. Express the volume of the cylinder as a polynomial function. The volume of a cylinder is .

This work, “Practice Exercises 7,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 7” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 6

SECTION 1.4

For the following exercise, identify the degree of the polynomial.

1.

For the following exercise, find the sum or difference.

2.

For the following exercise, find the product.

3.

For the following exercise, expand the binomial.

4.

For the following exercise, multiply the binomials.

5.

For the following exercise, multiply the polynomials.

6.

SECTION 1.5

For the following exercise, find the greatest common factor.

7.

For the following exercise, factor by grouping.

8.

For the following exercise, factor the polynomial.

9.

For the following exercise, factor the polynomials.

10.

For the following exercise, consider the following scenario:

A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yd. as shown in the figure below. The flagpole will take up a square plot with area .

11. Find the length of the base of the flagpole by factoring.

SECTION 1.6

For the following exercise, simplify the rational expression.

12.

For the following exercise, multiply the rational expressions and express the product in simplest form.

13.

For the following exercise, divide the rational expressions.

14.

For the following exercise, add and subtract the rational expressions, and then simplify.

15.

For the following exercise, simplify the rational expression.

16.

Real-World Applications

17. The area of Lijuan’s yard is ft2. A patch of sod has an area of ft2. Divide the two areas and simplify to find how many pieces of sod Lijuan needs to cover her yard.

This work, “Practice Exercises 6,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 6” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 8

SECTION 5.4

Algebraic

For the following exercise, use long division to divide. Specify the quotient and the remainder.

1.

For the following exercise, use synthetic division to find the quotient. Ensure the equation is in the form required by synthetic division. (Hint: Divide the dividend and divisor by the coefficient of the linear term in the divisor. Make sure the coefficient for the divisor is 1.)

2.

Graphical

For the following exercise, use the graph of the third-degree polynomial and one factor to write the factored form of the polynomial suggested by the graph. The leading coefficient is 1.

3. Factor is

Extensions

For the following exercise, use synthetic division to determine the quotient involving a complex number.

4.

Real-World Applications

For the following exercise, use the given volume of a box and its length and width to express the height of the box algebraically.

5. Volume is , length is , width is .

For the following exercise, use the given volume and radius of a cylinder to express the height of the cylinder algebraically.

6. Volume is , radius is .

SECTION 5.5

Algebraic

For the following exercise, use the Remainder Theorem to find the remainder.

7.

For the following exercise, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.

8.

For the following exercise, use the Rational Zero Theorem to find the real solution(s) to the equation.

9. .

For the following exercise, find the complex solutions (real and non-real).

10.

Numeric

For the following exercise, list all possible rational zeros for the function.

11.

Real-World Applications

For the following exercise, find the dimensions of the box described.

12. The length is 3 times the height and the height is 1-inch less than the width. The volume is 108 cubic inches.

For the following exercise, find the dimensions of the right circular cylinder described.

13. The radius and height differ by 1 meter. The radius is larger and the volume is cubic meters.

SECTION 5.6

Algebraic

For the following exercise, find the domain, vertical asymptote, and horizontal asymptote of the function.

14.

For the following exercise, describe the local and end behavior of the function.

15.

For the following exercise, find the slant asymptote of the function.

16.

Graphical

For the following exercise, use the given transformation to graph the function. Note the vertical and horizontal asymptotes.

17. The reciprocal squared function shifted down 2 units and right 1 unit.

Graphical

For the following exercise, find the horizontal intercept, the vertical intercept, the vertical asymptote, and the horizontal or slant asymptote of the function. Use that information to sketch a graph.

18.

For the following exercise, write an equation for a rational function with the given characteristics.

19. Vertical asymptotes at ,

x-intercepts at (-2,0) and (1,0). Horizontal asymptote at .

For the following exercise, use the graph to write an equation for the function.

20.

Extensions

For the following exercise, identify the removable discontinuity.

21.

This work, “Practice Exercises 8,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 8” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 2

SECTION 2.1

For the following exercise, find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept.

1.

For the following exercise, solve the equation for y in terms of x.

2.

For the following exercise, find the distance between the two points. Simplify your answer, and write the exact answer in simplest radical form for irrational answers.

3.

For the following exercise, find the coordinates of the midpoint of the line segment that joins the two given points.

4.

For the following exercise, plot the three points on the given coordinate plane. Draw a line between the two endpoints and state whether the three points you plotted appear to be collinear (on the same line).

5.

For the following exercise, construct a table and graph the equation by plotting at least three points.

6.

For the following exercise, find and plot the x- and y-intercepts, and graph the straight line based on those two points.

7.

Technology

For the following exercise, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2nd CALC button and 1:value button, hit enter. At the lower part of the screen you will see “x=” and a blinking cursor. You may enter any number for x and it will display the y value for any x value you input. Use this and plug in x = 0, thus finding the y-intercept, for each of the following graphs.

If you are using the

Desmos calculator

, then enter the equation. The graphed line will appear in the coordinate plane. You will see two dots representing the

x and

y intercepts. Place your cursor over the dot representing the

y intercept and write down the order pair.

8. .

SECTION 2.2

For the following exercise, solve the equation for

x.

9.

For the following exercise, solve each rational equation for

x. State all x-values that are excluded from the solution set.

10.

For the following exercise, find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form.

11.

For the following exercise, find the equation of the line using the given information.

12. The slope is and it passes through the point

For the following exercise, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither.

13.

Numeric

For the following exercise, find the slope of the line that passes through the given points.

14.

For the following exercise, find the slope of the lines that pass through each pair of points and determine whether the lines are parallel or perpendicular.

15. ;

SECTION 2.3

Real-World Applications

For the following exercise, use the information to find a linear algebraic equation model to use to answer the question being asked.

16. Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?

For the following exercise, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.10/min for calls.

17. Find the model of the total cost of Company B’s plan, using

m for the minutes.

For the following exercise, use this scenario: A retired woman has $50,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%.

18. Let

x be the amount the woman invests in the15% bond, and 50,000 –

x the amount the woman invests in the CD. Set up and solve the equation for how much the woman should invest in each option to sustain a $6,000 annual return.

For the following exercise, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $75/wk plus $.10/mi driven. Plan B charges $100/wk plus $.05/mi driven.

19. Write the model equations for the cost of renting a truck with plan A.

For the following exercise, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

20. Use the formula to find the radius of a cylinder with a height of 36 and a volume of

This work, “Practice Exercises 2,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 2” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 5

SECTION 3.5

Algebraic

For the following exercise, write a formula for the function obtained when the graph is shifted as described.

1. is shifted down 4 units and to the right 3 units.

For the following exercise, describe how the graph of the function is a transformation of the graph of the original function

f.

2.

Graphical

For the following exercise, use the graph of shown in the figure below to sketch a graph of the transformation of the

f(x).

3.

For the following exercise, sketch a graph of the function as a transformation of the graph of one of the toolkit functions.

4.

For the following exercise, write an equation for the graphed function by using transformations of the graphs of one of the toolkit functions.

5.

For the following exercise, use the graph of the transformed toolkit function to write a formula for the resulting function.

6.

For the following exercise, determine whether the function is odd, even, or neither.

7.

For the following exercise, describe how the graph of the function is a transformation of the graph of the original function

f.

8.

For the following exercise, write a formula for the function that results when the graph of a given toolkit function is transformed as described.

9. The graph of is vertically stretched by a factor of 8, then shifted to the right 4 units and up 2 units.

For the following exercise, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.

10.

SECTION 4.1

For the following exercise, determine whether the equation of the curve can be written as a linear function.

11.

For the following exercise, determine whether the function is increasing or decreasing.

12.

For the following exercise, find the slope of the line that passes through the two given points.

13.

For the following exercise, find a linear equation satisfying the conditions, if possible.

14.

For the following exercise, determine whether the lines given by the equations are parallel, perpendicular, or neither

15.

For the following exercise, find the x- and y-intercepts of the equation.

16.

For the following exercise, use the descriptions of the pair of lines to find the slopes of Line 1 and Line 2. Is the pair of lines parallel, perpendicular, or neither?

17. Line 1: Passes through (1,7) and (5,5). Line 2: Passes through (-1,-3) and (1,1)

For the following exercise, write an equation for the line described.

18. Write an equation for a line perpendicular to and passing through the point (-4,-1).

For the following exercise, write an equation for the line graphed.

19.

For the following exercise, sketch a line with the given features.

20. A

y-intercept of (0,5) and slope .

For the following exercise, write the equation of the line shown in the graph.

21.

SECTION 4.2

For the following exercise, consider this scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped to 4,700. Assume this trend continues.

22. Identify the year in which the population will reach 0.

For the following exercise, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted.

23. Find a reasonable domain and range for the function.

Real-World Applications

24. In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured to be 285. The population changed linearly. Let the input be years since 2003.

a. Find a formula for the owl population,

P. Let the input be years since 2003.

b. What does your model predict the owl population to be in 2012?

25. When hired at a new job selling electronics, you are given two pay options:

Option A: Base salary of $10,000 a year with a commission of 9% of your sales.

Option B: Base salary of $19,000 a year with a commission of 4% of your sales.

Write a model for each option. How much would you need to sell for option A to produce a larger income?

SECTION 4.3

For the following exercise, draw a scatter plot for the data provided. Does the data appear to be linearly related?

26.

100

250

300

450

600

750

12

12.6

13.1

14

14.5

15.2

For the following exercise, draw a best-fit line for the plotted data.

27.

Numeric

28. The U.S. Census tracks the percentage of persons 25 years or older who are college graduates. That data for several years is given in the table below. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the percentage exceed 35%?

Year

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

Percent Graduates

21.3

21.4

22.2

23.6

24.4

25.6

26.7

27.7

28

29.4

For the following exercise, consider this scenario: The population of a city increased steadily over a 10-year span. The following ordered pairs shows the population and the year over the 10-year span (population, year) for specific recorded years:

29. Use linear regression to determine a function,

y, where the year depends on the population. Round to three decimal places of accuracy. Predict when the population will hit 8,000.

This work, “Practice Exercises 5,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 9

SECTION 6

.1

Algebraic

For the following exercise, identify whether the statement represents an exponential function. Explain.

1. The height of a projectile at time is represented by the function .

For the following exercise, consider this scenario: For each year the population of a forest of trees is represented by the function In a neighboring forest, the population of the same type of tree is represented by the function (Round answers to the nearest whole number.)

2. Which forest had a greater number of trees initially? By how many?

For the following exercise, determine whether the equation represents exponential growth, exponential decay, or neither. Explain.

3.

For the following exercise, find the formula for an exponential function that passes through the two points given.

4.

For the following exercise, use the compound interest formula, .

5. After a certain number of years, the value of an investment account is represented by the equation What is the value of the account?

Numeric

For the following exercise, evaluate each function. Round answers to four decimal places, if necessary.

6. , for

Technology

For the following exercise, use a graphing calculator to find the equation of an exponential function given the points on the curve.

7. .

Real-World Applications

8. A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After 35 hours, 50 mg of the substance remains. How many milligrams will remain after 54 hours?

9. Kyoko has $10,000 that she wants to invest. Her bank has several investment accounts to choose from, all compounding daily. Her goal is to have $15,000 by the time she finishes graduate school in 6 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal? (Hint: Solve the compound interest formula for the interest rate. Note: banks use 360 for

n when compounded daily.)

SECTION 6.2

For the following exercise, graph each set of functions on the same axes.

10. .

For the following exercise, graph the function and its reflection about the x-axis on the same axes.

11.

For the following exercise, graph the transformation of Give the horizontal asymptote, the domain, and the range and describe the end behavior.

12. .

For the following exercise, start with the graph of Then write a function that results from the given transformation.

13. Reflect about the

x axis.

Numeric

For the following exercise, evaluate the exponential function for the indicated value of

x.

14. .

Technology

For the following exercise, use a graphing calculator to approximate the solution of the equation. Round to the nearest thousandth.

15. .

SECTION 6.3

Algebraic

For the following exercise, rewrite the log equation in exponential form and the exponential equation in logarithmic form.

16.

Numeric

For the following exercise, evaluate the base logarithmic expression without using a calculator.

17.

For the following exercise, evaluate the natural logarithmic expression without using a calculator.

18.

Real-World Applications

19. The exposure index for a camera is a measurement of the amount of light that hits the image receptor. It is determined by the equation where

f is the “f-stop” setting on the camera, and

t is the exposure time in seconds. Suppose the f-stop setting is and the desired exposure time is seconds. What will the resulting exposure index be?

SECTION 6.4

Algebraic

For the following exercise, state the domain, vertical asymptote, and end behavior of the function.

20.

Graphical

For the following exercise, sketch the graphs of the pair of functions on the same axis.

21.

For the following exercise, sketch the graph of the indicated function.

22.

For the following exercise, write a logarithmic equation corresponding to the graph shown.

23. Use as the parent function.

Technology

For the following exercise, use a graphing calculator to find an approximate solution to the equation.

24.

This work, “Practice Exercises 9,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 4

SECTION 3

.1

For the following exercise, determine whether the relation represents

y as a function of

x.

1.

For the following exercise, evaluate .

.

2.

Graphical

For the following exercise, use the vertical line test to determine which graphs show relations that are functions.

3.

4. Given the following graph:

a. Evaluate

b. Solve for

For the following exercise, determine if the given graph is a one-to-one function.

5.

Numeric

For the following exercise, determine whether the relation represents a function.

6.

For the following exercise, determine if the relation represented in table form represents

y as a function of

x.

7.

x

5

10

15

y

3

8

8

For the following exercise, evaluate the function

f at the values .

8.

For the following exercise, graph on the given domain. Determine the corresponding range. Show the graph.

9.

Real-World Applications

10. The amount of garbage produced by a city with population is given by is measured in tons per week, and population is measured in thousands of people.

a. The town of Tola has a population of 40,000 and produces 13 tons of

garbage each week. Express this information in terms of the function

f.

b. Explain the meaning of the statement

SECTION 3.2

For the following exercise, find the domain of the function using interval notation.

11.

Graphical

For the following exercise, write the domain and range of the function using interval notation.

12.

For the following exercise, sketch a graph of the piecewise function. Write the domain in interval notation.

13.

For the following exercise, given the function

f, evaluate

14.

For the following exercise, write the domain for the piecewise function in interval notation.

15.

SECTION 3.3

For the following exercise, find the average rate of change of the function on the interval specified for real numbers

b or

h in simplest form.

16.

For the following exercise, consider the graph of

f shown below.

17. Estimate the average rate of change from to to .

For the following exercise, use the graph of the function to estimate the intervals on which the function is increasing or decreasing.

18.

Numeric

19. The table below gives the annual sales (in millions of dollars) of a product from 1998 to

2006.

Year

1998

1999

2000

2001

2002

2003

2004

2005

2006

Sales (millions of dollars)

201

219

233

243

249

251

249

243

233

What was the average rate of change of annual sales

a. Between 2001 and 2002?

b. Between 2001 and 2004?

For the following exercise, find the average rate of change of the function on the interval specified.

20.

Technology

For the following exercise, use a graphing utility to estimate the local extrema of the function and to estimate the intervals on which the function is increasing and decreasing.

21.

Real-World Applications

22. At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125. Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?

SECTION 3.4

For the following exercise, determine the domain for the function in interval notation.

23. Given find

f +

g,

f –

g,

fg,

For the following exercise, use the pair of functions to find

f(g(x)) and

g(f(x)). Simplify your answer.

24.

For the following exercise, use the set of functions to find

f(g(h(x))). Simplify your answer.

25.

For the following exercise, find functions

f(x) and

g(x) so the given function can be expressed as

h(x)=f(g(x).

26.

Graphical

For the following exercise, use the graphs of

f shown in Figure 1 and

g shown in Figure 2 to evaluate the expression.

Figure 1

Figure 2

27.

For the following exercise, use graphs of

f(x) shown in Figure 3,

g(x) shown in Figure 4, and

h(x) shown in Figure 5 to evaluate the expression.

Figure 3

Figure 4

Figure 5

28.

For the following exercise, use the function values for

f and

g shown in the table below to evaluate the expression.

x

f(x)

g(x)

-3

11

-8

-2

9

-3

-1

7

0

0

5

1

1

3

0

2

1

-3

3

-1

-8

29.

For the following exercise, use the pair of functions to find

f(g(0)) and

g(f(0)).

30.

Real-World Applications

31. A store offers customers a 30% discount on the price

x of selected items. Then, the store takes off an additional 15% at the cash register. Write a price function

P(x) that computes the final price of the item in terms of the original price

x. (Hint: Use function composition to find your answer.)

This work, “Practice Exercises 4,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 4” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Technology Activity 5—Example

*Note: This document is to be used as a reference accompanying the Technology Activity 5 instructional video.

Do not use the same isotope used in this example.

We are now going to investigate exponential regression using

Desmos calculator

.

The first thing we are going to do is add our data set into a table in Desmos. In the input 1 line, type in

table. Desmos will start the table.

Enter your data into the table.

Adjust the view of the graph by clicking the

Zoom Out icon on the right side (see the figure below). Zoom out until all your data points are displayed in the grid.

Adjust your

x and

y values accordingly. All isotope

y values will range from -25 to 1050. The

x values will range from -1000 or -100 or -10, it all depends on your smallest

x value. If your smallest

x value (besides 0) is between 1 and 10 then go with a -10; if the smallest

x value is in between 10 and 100 go with -100; if the smallest

x value is in between 100 and 1000 then go with -500; if the smallest value is in between 1000 and 10,000 then go with -1000. Likewise for the largest

x value go with 10, 100, 1000, or 10,000 more than the largest

x value. The step should also be based on the values of

x for your isotope. For our isotope, we set

x values to with a step of 10,000. To set the

x and

y ranges click on the

Graph Settings icon.

Then enter your ranges for

x and

y as discussed above.

We can also add labels to the

x and

y axes based on the time (years or days) and “Amount” for the

y axis.

We will now enter an exponential expression based on the initial value of our data set. For example, if our initial value/amount is 1000 then we will enter . Desmos will ask us to create a slider for

r.

Click on “

add slider

r”

Adjust your slider values so that you can determine the best exponential fit for your data. Small increments of

r makes it easier to adjust the graph accordingly. The slider values for your isotope were given in the table of isotopes. Values given will be the slider minimum, maximum, and the step. Click on the slider and press the TAB key to get to the minimum slider input area.

Press the TAB key again to get to the maximum slider input area.

Press TAB key a third time to get to the Step input area.

You edit the color of your points by clicking on the circle to the left of

y and holding the mouse button down until the edit box comes up.

Select the color you want and then press the ENTER key.

When you are done adjusting the slider, enter your final regression equation as

y = …

Regression equation:

Export your graph to be turned in. Save your project and make sure to share it with your Mentor for grading.

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MAT-121: COLLEGE ALGEBRA

Technology Activity 3—Example

*Note: This document is to be used as a reference accompanying the Technology Activity 3 instructional video.

Do not use the same data set used in this example.

We are now going to investigate linear regression using

Geogebra classic

.

The first thing we need to do is to set the axes values based on our data set. Click on the

Tools icon in the upper right area of the grid.

We should see the following screen. Click on the

settings icon.

We can now set the

x and

y axes values based on our data set values.

After you have set your values click on the X to close out

Tools. Click on the

Input area to the left and start entering your ordered pairs.

When you enter ( Geogebra will automatically pair it up with a ). Jut enter the ordered pair and press the ENTER key

The point will be displayed in the grid and Geogebra will move us down to the next

Input line for our next ordered pair.

After you have entered all your data points you should have a scatter plot that looks something like the following (note: if your data set values decrease you will have a scatter plot with a negative slope.)

We will now visually select our best line of fit. Make sure the

Point icon is selected as in the above figure (should be since the last thing we did was enter a point.) Click to the lower left (or upper left) of your scatter plot at where you think the best line of fit should start. Geogebra will place a point there, label it the next letter in line and place its ordered pair values below the last point you manually entered.

We are now going to change the color of this point so that we know it is the one we selected for our visual best line of fit. To do this right click on the point in the grid. The following screen will be displayed. We want to click on

Settings.

The settings are displayed on the right. Click on the

Color tab and selected a color different than the one in the scatter plot. We will select red.

After you have made your choice click the X to close out the settings window.

We are now ready to visually select our line of best fir. Click on the

Line tool icon and select

Line.

Next click on your point you entered visually and adjust your line to what you think the best fit should be (this should be based on trying to have as many points on your line or as close as possible.)

Finish the line by clicking again. Geogebra will display the equation of your line in the

Input area on the left below your visual point. Above the equation of the line is the second point based on when you clicked to complete your line. You can change the color of this point to match the other one.

We will now make the line the same color as our two points. Right click on the line, select

Settings and then

Color and select the same color as the points. Close out the settings window.

We are now ready to have Geogebra determine our best line of fit. Click on the

Perpendicular Line tool icon and select

Best Fit Line.

We are now going to select the region we want Geogebra to determine the best fit line. Click in the upper left corner or your scatter plot and drag your mouse down to include the lower right area. We are selecting a rectangular area just like many other applications do.

After you have selected your region, lift your finger off the left mouse button and the line will appear in your grid along with its equation to the left.

Your lines won’t exactly match up, but there will probably be an area in the middle where the lines cross as shown above. Save your project, to be turned in.

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MAT-121: COLLEGE ALGEBRA

Technology Activity 4—Example

*Note: This document is to be used as a reference accompanying the Technology Activity 4 instructional video.

Do not use the same polynomial used in this example.

Given .

Let a0 and an be nonzero. Then each rational solution x can be written in the form for p and q satisfying two properties:

1. p is an integer factor of a0, and

2. q is an integer factor of the coefficient an.

1.

Given (enter your polynomial here):

Enter your polynomial cleared of fractions:

Graph your polynomial using

Geogebra

.

a. Possible values of p:_____________________

b. Possible values of q:_____________________________

c. Possible values of :___________

d. Values of for which the function value is zero:________________________

e. Zero(s) from the graph:______________________

g. Rational roots of :___________________________________

Synthetic Division Using Rational Zeros

Using our two zeros above, we will perform synthetic division to divide our 4th degree polynomial to a 3rd degree polynomial and then a quadratic polynomial. This will allow us to factor or use the quadratic formula to find the complex zeros/roots.

j. State the quadratic polynomial: __________________________

k. Identify any complex zeros for the polynomial:____________________________

Descartes’ Rule of Signs

Descartes’ Rule of Signs tells us of a relationship between the number of sign changes in and the number of positive real zeros.

Given any polynomial,

f(x),

1. Write it with the terms in descending order, i.e. from the highest degree term to the lowest degree term, .

2. Count the number of sign changes of the terms in

f(x). Call the number of sign changes

n.

3. Then the number of

positive roots of

f(x) is less than or equal to

n

4. Further, the possible number of positive roots is

n,n−2,n−4,…

For example, if there were 3 sign changes then there would be 3 or 1 (3-2) positive real roots. If there were 4 sign changes then there would be 4, 2, or 0 positive real roots.

For place the signs of each term here (do not forgot the sign of the first term): + – + – –

State the number of sign changes: 3

State the number of possible positive real roots using the above information: 3, 1

There is a similar relationship between the number of sign changes in

p(-x) and the number of negative real zeros.

Note: If the exponent (degree) of a term is odd then

-x will yield a negative value. For example, if our term was , then since 2 negatives make a positive. For even exponents (degree) then the term will be the sign in front of the coefficient. For example, .

For place the signs of each term here (do not forgot the sign of the first term): + + + + –

State the number of sign changes: 1

State the number of possible negative real root using the above information: 1

So, combining the positive and negative possible roots we see that we have 4 (3+1) or 2 (1+1) real zeros. We know from above that we had 2 real roots.

Place a copy of your graph of the original polynomial after finding all the roots/zeros and

y-intercept). Make sure to include the extrema point on the graph as well.

Let’s verify our special points by using Geogebra. Bring up

Geogebra Classic

. Enter your polynomial.

You may have to click on the

Zoom Out icon to see the complete graph. Click on the 3 vertical dots to the right of your polynomial and select

Special Points.

Verify that the roots and extrema you found in Desmos (especially our visually selected extrema) are the same.

State the 4 special points from Geogebra: (-0.25, 0), (2, 0), (1.13, -6.34) (0, -2)

Create a table of positive/negative values on each side of a real root/zero to determine if the graph is above/below the root/zero. You can also use your graph in Desmos to determine this:

Interval

Test Point

Value of

f(

x)

Sign of

f(

x)

Graph above or below

x-axis

-1

+

Above

0

-2

–

Below

3

+

Above

Determine end behavior of the polynomial

Using your graph in Desmos, state what

f(x) approaches as

x approaches -∞:

Using your graph in Desmos, state what

f(x) approaches as

x approaches ∞:

State the

y-intercept (in ordered pair format):

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MAT-121: COLLEGE ALGEBRA

Technology Activity 2—Example

*Note: This document is to be used as a reference accompanying the Technology Activity 2 instructional video.

Do not use the equations used in this example.

This technology activity will utilize the graphing and solving capabilities of

Geogebra’s Classic graphing utility

and

Desmos

.

Quadratics Equations

Step 1: We will investigate quadratic equations using Geogebra. Enter the quadratic equation you selected from the list where it says “+ Input” in Geogebra. If all of the graph is not displayed in the grid, then use the “zoom out” icon to zoom out until all of the graph is displayed in the grid. We have entered .

Step 2: Solve your quadratic equation using either factoring, completing the square, or the quadratic formula. Place your solutions down below. These “solutions” are also known as

x-intercepts, and zeros (since they make the

y coordinate of the

x-intercept equal to 0.)

Algebra:

Factors of 2: 1,2; -1,-2

Factors of -20: 1,-20; -1,20; 2,-10; -2,10; 4,-5; -4,5

Factors that add to -3 are: 1 with 5 and 2 with -4: (x-4)(2x+5)

Solution 1: _____

x = 2.5___________________ Solution 2: ____

x = 4________________

Step 3: With your quadratic equation in general form , we can use the coefficients of the squared term and the linear term to find the coordinates of the vertex. To find the

x coordinate of the vertex use this formula: . To find the

y coordinate of the vertex just plug the preceding

x value into the quadratic equation. Write the coordinates of the vertex and the

y-intercept below.

General form: __________________________

a: _____

2______ b: ___

-3______

Vertex: _________________

Y-intercept: ______

(0, -20)___________

Step 4: Now we will use the tools in Geogebra to verify our results from steps 3 and 4. Click the 3 vertical dots to the right of your quadratic equation and select

Special Points.

Step 5: Verify the values in Geogebra are the same as the ones above. Note that

Root represents the

x-intercepts,

Extremum represents the vertex, and

Intersect represents the

y-intercept. Write the values below.

Root: ___

(-2.5, 0)_________ and _____

(4, 0)__________

Extremum: _____

(0.75, 21.13)____________

Intersect: ______

(0, -20)_______

Step 6: Save your file. For the next investigation for this activity we will be using Desmos.

Linear Inequalities

Navigate to the Desmos calculator by clicking on the following link:

Desmos calculator

. To get help using Desmos click on the question mark icon in the upper right corner.

Step 7: Click on the

tools icon

and uncheck the

Y-axis so we are sort of dealing with just a number line (though our inequalities will be shaded.)

Step 8: Enter the first inequality in #1 space (see figure below). Since Desmos (and most online graphing utilities) are 2-D (dimensional) our inequalities will show up shaded and we will need to properly interpret them when we graph them on our number line. If the area is shaded to the left and the vertical line is dotted then that means solution is < (strictly less than); shaded to the left and solid vertical line then that means ≤ (less than or equal to); if the area is shaded to the right with a dotted vertical line then that means > (strictly greater than); if the area is shaded to the right with a solid vertical line then that means ≥ (greater than or equal to)

Note: For the less than or equal to and the greater than or equal to inequalities you will need to type them in as <= and >= and Desmos will change them to respectively.

Enter:

Step 9 Hover the mouse cursor over the gray dot on the number line to find the

x value for the solution to the inequality. Depending on if the vertical line is dotted or solid and the area is shaded to the right or to the left, write the solution to your first inequality below. Below your solution, write the original inequality and show the algebra to find the solution. Verify your algebraic solution is the same as the one you just found in Desmos. Then graph your solution on the number line provided below.

Solution: _____

x ≤ 0.75 ______________

Original inequality: _______

3x + 2 ≥ 7x – 1_______________

Algebraic steps for solution:

Add -3x to both sides: -3x + 3x + 2 ≥ 7x – 3x – 1

Simplify: 2 ≥ 4x – 1

Add 1 to both sides: 1 + 2 ≥ 4x – 1 + 1

Simplify: 3 ≥ 4x

Divide both sides by 4:

Simplify: ¾ ≥ x or reading from right to left x ≤ ¾

Graphed solution:

Step 10: Click on the circle to the left of your inequality to remove it from the grid without removing your inequality. Repeat the above process for your other 3 inequalities.

Step 11: You can save your graph by clicking the

Save button in the upper left corner.

Step 12: Your graph can also be shared.

Click on the

Share graph icon in the upper right corner.

Step 13: Next, click on the

Copy button to share the link with your mentor. Paste the link in the space below.

Shared link: ____________https://www.desmos.com/calculator/wbrrquuk3p__________

Step 14: Click on the

Export image icon to export your graph to your computer to be uploaded along with all your other files for this activity. Pick any

Size and

Line thickness and then click the

Download PNG button.

Absolute Value Inequalities

Absolute value

inequalities will give us solutions very similar to compound inequalities. There will either be a shaded region between two values (representing an AND compound inequality) or two separate shaded regions (representing an OR compound inequality.)

Step 15: Start with a new blank graph. Click on the 3 horizontal bars in the upper left (Open Graph) and then click on New Blank Graph.

Step 16: Like compound inequalities, absolute value inequalities will show up shaded and we will need to properly interpret them when we graph them on our number line. For example, let’s solve algebraically. The greater than, >, or greater than or equal to,≥, is an example of an OR compound inequality. Refer to page 177 in the book PDF document.

Step 17: Using Desmos we see the shaded region that represents our two solutions.

Solution (write in both interval and set builder notation): , or

Note: For the set builder notation, In words this says: “The set of

x such that

x is less than -1 OR

x is greater than 3.” For the second set builder notation, this says: “The set of

x such that

x is an element of the set of Real Numbers (or

x is a Real Number),

x is less than -1 OR

x is greater than 3.”

Original absolute value inequality: __ ____________________

Algebraic steps for solution: Using the above definition we get:

Graphed solution:

Step 18: Enter the first absolute value inequality in #1 space in Desmos. You will get a shaded region(s) representing the two solutions.

Step 20: Write the solution to your first absolute value inequality below. Below your solution, write the original absolute value inequality and show the algebra to find the solution region. Verify your algebraic solution is the same as the one you just found in Desmos. Then graph your solution on the number line provided below.

Step 21: Click on the

Export image icon to export your graph to your computer to be uploaded along with all your other files for this activity. Pick any

Size and

Line thickness and then click the

Download PNG button.

Step 22: Click on the circle to the left of your absolute value inequality to remove it from the grid without removing your inequality.

Step 23: We are now going to investigate the other types of absolute value inequality, . Enter

Step 24: Algebraic steps for solution: Using the above definition we get:

or

Solution (write in both interval and set builder notation): , or

Note: For the set builder notation, In words this says: “The set of

x such that

x is greater than or equal to AND

x is less than or equal to .” For the second set builder notation, this says: “The set of

x such that

x is an element of the set of Real Numbers (or

x is a Real Number),

x is greater than or equal to AND

x is less than or equal to .” ”

Step 25: Click on the

Export image icon to export your graph to your computer to be uploaded along with all your other files for this activity. Pick any

Size and

Line thickness and then click the

Download PNG button.

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MAT-121: COLLEGE ALGEBRA

Technology Activity 1—Example

*Note: This document is to be used as a reference accompanying the Technology Activity 1 instructional video.

Do not use the points and/or equations used in this example.

This technology activity will utilize the graphing and solving capabilities of

Geogebra’s Classic graphing utility

.

Investigation of Parallel and Perpendicular Lines

This activity will thoroughly investigate parallel and perpendicular lines.

Step 1: Using the

point icon tool (refer to the user’s document) place two points in the coordinate plane (grid.) These two points should be labeled

A and

B (make sure the coordinates of the ordered pairs are integer values which will make the calculations easier.)

Make sure the two points will create a line with positive slope. Write down the two ordered pairs.

A: _____

(-6, -2)_______ B:_____

(2, 4)_________

Step 2: Click the

line icon tool and select

Line. Then click on the two points, beginning with

A, in the coordinate plane (grid.) Make sure to click exactly on each point so your equation that is displayed has integer values. Write the equation given in Geogebra (should be in standard form)

Standard form: ___

-3x + 4y = 10________________

Step 3: Click the

angle icon

and select

Slope. Click on point

A to obtain the slope of the line. Note: Your slope may be given as a decimal value.

Slope:_______________________

Step 4: Rewrite the equation given in standard form in Geogebra into slope-intercept form. Also, give the slope in non-decimal form (ie. as a fraction representing rate of change.)

Show all the algebra steps.

Add 3x to both sides: -3x + 3x + 4y = 3x + 10

Simplify: 4y = 3x + 10

Divide both sides by 4:

Simplify:

Slope-intercept form: _______

y = (¾) x + 5/2___________________

Non-decimal slope: _________

Step 5: Click on the space to the right of the + sign (says “

Input”) and enter an equation for a parallel line with a different

y-intercept from the first equation. Your lines should be parallel. Write the equation you entered below.

Slope-intercept form: _______

y = (¾) x – 2________________

Step 6: To verify your lines are parallel, use the

Slope tool to verify the slopes are the same.

Step 7: Save your graph by clicking on the

File icon

and select

Export Image to be uploaded for verification.

step 8: Click on the circles to the left of the second equation and its slope to remove them from the grid. The circles should have no color at all (white background)

Step 9: We will now use the

Parallel Line option under the

Perpendicular Line icon. Click the

Perpendicular Line icon and select

Parallel Line option. Click on the line in the grid/graph and notice how it becomes a little more thicker. Drag your mouse exposing the parallel line and place it so it will have the same

y-intercept that you have/had in the second equation that had been removed. If your line is slightly off (like shown below), then adjust point

C to have the

y-intercept of the previous second line by clicking on its ordered pair coordinates and enter the values for the

y-intercept. Press the ENTER key on your computer. This should automatically adjust your line’s equation to the correct values.

Step 10: Use the

Slope icon

tool to verify the slope of the second line is the same as the first line. Export the image to be uploaded at the end of the activity with all the other uploads. Make sure your exported images have different names.

Step 11: Write the equation of the line (standard form) given in Geogebra.

Standard form: _____

-3x + 4y = -8_______________________

Step 12: Rewrite the above equation in

y-intercept form

showing all algebra steps. Verify your equation matches.

Add 3x to both sides: -3x + 3x + 4y = 3x – 8

Simplify: 4y = 3x – 8

Divide both sides by 4:

Simplify:

y- intercept form: _____

y = (¾)x – 2_______________________

Step 13: Click the

File icon tool and then click on the

Save option. If you receive a popup message about logging into your account then just dismiss it to get the

Save popup. Save the file to your computer, you will upload it as part of your submission for the activity. You may want to name it something to do with the positive slope of parallel lines because we are about to repeat the same process, but starting with two points that will give us a

negative slope.

Step 14: Click the

File icon tool and then click on the

+ New option.

Repeating Steps 1-14 Above:

Step 15: Using the

point icon tool (refer to the user’s document) place two points in the coordinate plane (grid.) These two points should be labeled

A and

B (make sure the coordinates of the ordered pairs are integer values which will make the calculations easier.)

Make sure the two points will create a line with negative slope. Write down the two ordered pairs.

A: ____

(-3, 5)__________ B:____

(4, 0)__________

Step 16: Click the

line icon tool and select

Line. Then click on the two points, beginning with

A, in the coordinate plane (grid.) Make sure to click exactly on each point so your equation that is displayed has integer values.

Step 17: Click the

angle icon

and select

Slope. Click on point

A to obtain the slope of the line. Note: Your slope may be given as a decimal value.

Slope:_______

-0.71________________

Step 18: Rewrite the equation given in standard form in Geogebra into slope-intercept form.

Show all the algebra.

Standard form: ____

5x + 7y = 20___________________

Add -5x to both sides: -5x + 5x + 7y = -5x + 20

Simplify: 7y = -5x + 20

Divide both sides by 7:

Simplify:

Slope-intercept form: ____

y = (-5/7)x + (20/7)______________________

Non-decimal slope: ___

-5/7______

Step 19: Click on the space to the right of the + sign (says “

Input”) and enter an equation for a parallel line with a different

y-intercept from the first equation. Your lines should be parallel. Your lines should be parallel. Enter your equation below.

Parallel equation: _____

y = (-5/7)x – 1_______________

Step 20: To verify your lines are parallel, use the

Slope tool to verify the slopes are the same. Save your graph by clicking on the

File icon

and select

Export Image to be uploaded for verification.

Step 21: Click on the circles to the left of the second equation and it’s slope to remove them from the grid. The circles should have no color at all (white background)

Step 22: We will now use the

Parallel Line option under the

Perpendicular Line icon. Click the

Perpendicular Line icon and select

Parallel Line option. Drag your mouse exposing the parallel line and place it so it will have the same

y-intercept that you have/had in the second equation that had been removed. If your line is slightly off (like shown below), then adjust point

C to have the

y-intercept of the previous second line by clicking on its ordered pair coordinates and enter the values for the

y-intercept. Press the ENTER key on your computer. This should automatically adjust your line’s equation to the correct values.

Step 23: Use the

Slope icon

tool to verify the slope of the second line is the same as the first line. Export the image to be uploaded at the end of the activity with all the other uploads. Make sure your exported images have different names.

Step 24: Write the equation of the line (standard form) given in Geogebra.

Standard form: ___

5x + 7y = -7_________________________

Step 25: Rewrite the above equation in

y-intercept form

showing all algebra steps. Verify your equation matches.

Add -5x to both sides: -5x + 5x + 7y = -5x – 7

Simplify: 7y = -5x – 7

Divide both sides by 7:

Simplify:

y- intercept form: ____

y = (-5/7) – 1________________________

Step 26: Click the

File icon tool and then click on the

Save option. If you receive a popup message about logging into your account then just dismiss it to get the

Save popup. Save the file to your computer, you will upload it as part of your submission for the activity. You may want to name it something to do with the negative slope of parallel lines.

Step 27: For all the items not associated with the first line, click on the 3 vertical dots and delete the items so we are left with only the first line and its items (A, B f: Line(A,B), m = Slope(f)). Note: your line may be labeled another letter other than f.

Perpendicular Lines:

Step 28: Perpendicular lines have a slope that is a negative reciprocal of the given line: , where represents the slope of the perpendicular line and is the slope of the given line. Using the slope of your first slope, create an equation that is perpendicular to the given (first line in Geogebra) line. Enter that equation below and then into Geogebra.

Perpendicular line: _______

y = (7/5) x + 1______________________

Step 29: Verify the slope are negative reciprocals by using the

Slope icon tool on the perpendicular line. Export the image so that it can be submitted with the active.

Step 30: Click on the circles for the items of the perpendicular line and slope (make sure you click on the

Arrow/Move icon before clicking on the circles or another slope will appear after the line has been removed from the grid.)

Step 31: Now using the

Perpendicular icon

, select the

Perpendicular Line option and then click on the given line to create a perpendicular line. Move the perpendicular line so that it passes through the origin. Adjust point

C so that its coordinates represent the origin.

Step 32: Use the

Slope icon tool on the perpendicular line to verify that the slopes of the two lines are negative reciprocals of each other.

Step 33: Write down the given equation in standard form then rewrite the given equation in

slope-intercept form.

Make sure to show all the algebra.

Standard form: ______

-7x + 5y = 5___________________

Add 7x to both sides: 7x – 7x + 5y = 7x+5

Simplify: 5y = 7x + 5

Divide both sides by 5:

Simplify:

Slope-intercept form: ______

y= (7/5)x__________________

Step 34: Save the file for submission. After saving the file, start a new one.

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resources_22sep/1.4 – 1.6 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 1.4–1.6

SECTI

ON 1.4

—POLYNOMIALS

Coefficient and Degree

Mathispower4u. (2009, November 2).

Introduction to polynomials

[Video]. YouTube.

Adding and Subtracting

Mathispower4u. (2014, August 10).

Adding and subtracting polynomials (l3.2)

[Video]. YouTube.

Multiplying

Mathispower4u. (2010, July 14).

Multiplying polynomials

[Video]. YouTube.

Khan Academy. (2019, July 24).

Multiplying monomials | Polynomial arithmetic | Algebra 2 | Khan Academy

[Video]. YouTube.

Khan Academy. (2020, February 10).

Area model for multiplying polynomials with negative terms

[Video]. YouTube.

Mathispower4u. (2009, November 5).

Special polynomial products

[Video]. YouTube.

Using Distributive Property

Mathispower4u. (2011, October 4).

Ex: Multiplying using the distributive property

[Video]. YouTube.

Mathispower4u. (2019, May 13).

Multiplying binomials and trinomials

[Video]. YouTube.

1.5 FACTORING POLYNOMIALS

Greatest Common Factor (GCF)

Mathispower4u. (2015, September 21).

Ex: Determine the GCF of two monomials (two variables)

[Video]. YouTube.

Mathispower4u. (2017, August 3).

Factor the GCF from a trinomial: 30x^3-36x^2+12x

[Video]. YouTube.

Trinomials, Leading Coefficient of 1

Mathispower4u. (2011, October 12).

Ex: Factor trinomials when a equals 1

[Video]. YouTube.

Mathispower4u. (2019, February 4).

Using the TI84 table to help factor trinomials with a = 1

[Video]. YouTube.

Trinomials, Leading Coefficient Not 1

Mathispower4u. (2011, October 12).

Ex: Factor trinomials when a is not equal to 1 – trial and error method

[Video]. YouTube.

Mathispower4u. (2011, October 12).

Ex: Factor trinomials when a is not equal to 1 – bottoms up method

[Video]. YouTube.

Factor by Grouping

Mathispower4u. (2014, December 14).

Ex 1: Factor a quadratic expression using grouping

[Video]. YouTube.

Perfect Square

Mathispower4u. (2010, November 23).

Factoring a perfect square trinomial

[Video]. YouTube.

Difference of Squares

Mathispower4u. (2010, November 23).

Factoring a difference of squares

[Video]. YouTube.

Sum/Difference of Cubes

Mathispower4u. (2010, July 8).

Factoring a sum or difference of cubes

[Video]. YouTube.

Factoring Expressions With Fractional or Negative Exponents

Mathispower4u. (2016, July 21).

Factor expressions with negative exponents

[Video]. YouTube.

Mathispower4u. (2016, July 21).

Factor expressions with fractional exponents

[Video]. YouTube.

1.6 RATIONAL EXPRESSIONS

Simplifying Rational Expressions

Mathispower4u. (2010. July 8).

Simplifying rational expressions

[Video]. YouTube.

Mathispower4u. (2016, June 22).

Simplify and give the domain of rational expressions

[Video]. YouTube.

Mathispower4u. (2011, December 8).

Ex 3: Simplify rational expressions

[Video]. YouTube.

Multiplying Rational Expressions

Mathispower4u. (2011, December 12).

Ex 1: Multiply rational expressions – monomials

[Video]. YouTube.

Mathispower4u. (2011, December 12).

Ex 4: Multiply rational expressions

[Video]. YouTube.

Dividing Rational Expressions

Mathispower4u. (2011, December 12).

Ex 1: Dividing rational expressions – monomials

[Video]. YouTube.

Mathispower4u. (2011, December 12).

Ex 2: Dividing rational expressions

[Video]. YouTube.

Adding and Subtracting Rational Expressions

Mathispower4u. (2016, June 22).

Add and subtract rational expressions with like denominators and give the domain

[Video]. YouTube.

Mathispower4u. (2018, April 10).

Add or subtract basic rational expressions with unlike denominators

[Video]. YouTube.

Mathispower4u. (2011, December 13).

Ex: Add and subtract rational expressions – opposite denominators

[Video]. YouTube.

Simplifying Complex Rational Expressions

Mathispower4u. (2012, November 9).

Ex 2: Simplify a complex fraction (variables)

[Video]. YouTube.

Mathispower4u. (2015, September 29).

Ex: Simplify a complex fraction with addition and subtraction and constant denominators

[Video]. YouTube.

resources_22sep/DF2_ stairs option_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Discussion Forum 2: Stairs Option

In this option of the activity, you will measure the rise and run of several steps (they should be the same.) Round your measurement to the nearest inch.

Measure, or calculate, the distance from the bottom step (floor level) to the top stair, and round to the nearest inch.

Distance from bottom step to top stair:

The distance can be calculated using the Pythagorean theorem and the rise and run values. Do not forget to count the top run of your stairs to determine the total number of runs (the number of rises and runs should be the same.) The total number of runs along with the diagonal distance calculated using the Pythagorean theorem can be used to calculate the distance/length of your stairs.

Calculate the slope from your rise and run measurements.

State the slope (rise over the run):

Find an ordered pair (

x2,

y2), such that the distance between the ordered pair and the y-intercept equals the distance measured above (from the floor level to the top of the stairs). Graph your ordered pairs and draw the line between them as shown in the diagram below.

State the coordinates of (

x2,

y2):

Using the two ordered pairs above, write the equation of the line for your stairs. Make sure to state the y-intercept in ordered pair format, not as a single value.

State the equation of your line (two-point form):

Take a photo of your stairs. Then post your measurements, graph, equation of the line, and your photo to the designated discussion forum.

Thoroughly comment on at

least two of your classmates’ posts. Verifying that the non-origin ordered pair is correct (calculate his/her measured distance), the slope and equation of the line are correct, and a photo and graph are submitted. If anything is in error, please let your classmates know.

image1

resources_22sep/6.5 – 6.8 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 6.5–6.8

SECTION 6.5—LOGARITHMIC PROPERTIES

Using the Product Rule for Logarithms

Mathispower4u. (2016, August 11).

Expand logarithms using the product rule for logs

[Video] YouTube.

Mathispower4u. (2016, August 11).

Expand logarithms using properties of logarithms (expressions)

[Video] YouTube.

Using the Quotient Rule for Logarithms

Mathispower4u. (2012, June 26).

Ex: Combine a sum and difference of two logarithms

[Video] YouTube.

Mathispower4u. (2011, December 27).

Ex 2: Combine a logarithmic expression into one logarithm

[Video] YouTube.

Mathispower4u. (2016, August 12).

Combine logarithms using properties of logarithms

[Video] YouTube.

Using the Power Rule for Logarithms

Khan Academy. (2011, November 8).

Logarithm of a power | Logarithms | Algebra II | Khan Academy

[Video] YouTube.

Intuitive Math. (2020, March 21).

Log power rule proof

[Video] YouTube.

Khan Academy. (2007, November 10).

Proof: a log b = log(b^a), log a – log b = log(a/b) | Logarithms | Algebra II | Khan Academy

[Video] YouTube.

Mathispower4u. (2010, July 15).

The properties of logarithms

[Video] YouTube.

Expanding Logarithmic Expressions

Mathispower4u. (2012, June 28).

Ex: Expand a logarithm containing a radical

[Video]. YouTube.

Mathispower4u. (2016, August 11).

Expand logarithms using properties of logarithms (expressions)

[Video] YouTube.

Mathispower4u. (2011, December 27).

Ex 1: Expand logarithmic expressions

[Video] YouTube.

Condensing Logarithmic Expressions

Mathispower4u. (2016, August 12).

Combine logarithms using properties of logarithms

[Video] YouTube.

Mathispower4u. (2012, June 26).

Ex: Combine a sum and difference of two logarithms

[Video] YouTube.

Using the Change-of-Base Formula for Logarithms

Mathispower4u. (2010, July 15).

Logarithms: Change of base formula

[Video] YouTube.

Mathispower4u. (2011, December 27).

Ex: Change of base formula to evaluate logarithmic expressions

[Video] YouTube.

SECTION 6.6—EXPONENTIAL AND LOGARITHMIC EQUATIONS

Using Like Bases to Solve Exponential Equations

Mathispower4u. (2010, July 15).

Solving exponential equations – Part 1 of 2

[Video] YouTube.

Mathispower4u. (2011, December 21).

Ex 4: Solve exponential equations using like bases – No logarithms

[Video] YouTube.

Mathispower4u. (2011, December 21).

Ex 6: Solve exponential equations using like bases – No logarithms

[Video] YouTube.

Solving Exponential Equations Using Logarithms

Mathispower4u. (2010, July 15).

Solving exponential equations – Part 1 of 2

[Video] YouTube.

Mathispower4u. (2010, July 15).

Solving exponential equations – Part 2 of 2

[Video] YouTube.

Mathispower4u. (2011, December 29).

Ex 1: Solve exponential equations using logarithms

[Video] YouTube.

Using the Definition of a Logarithm to Solve Logarithmic Equations

Mathispower4u. (2012, June 26).

Ex: Solve a basic logarithmic equation – Linear and quadratic

[Video] YouTube.

Mathispower4u. (2012, June 26).

Ex: Solve a logarithmic equation with a sum – Quadratic formula

[Video] YouTube.

Using the One-to-One Property of Logarithms to Solve Logarithmic Equations

Mathispower4u. (2010, July 15).

Solving logarithmic equations

[Video] YouTube.

Solving Applied Problems Using Exponential and Logarithmic Equations

Mathispower4u. (2016, August 12).

Logarithm application: Magnitude of an earthquake

[Video] YouTube.

Mathispower4u. (2011, December 29).

Ex: Exponential function application with logarithms

[Video] YouTube.

SECTION 6.7—EXPONENTIAL AND LOGARITHMIC MODELS

Modeling Exponential Growth And Decay

Mathispower4u. (2014, November 29).

Introduction to exponential functions in the form f(x)=ae^(kx) – Part 1

[Video] YouTube.

Mathispower4u. (2014, November 29).

Introduction to exponential functions in the form f(x)=ae^(kx) – Part 2

[Video] YouTube.

Mathispower4u. (2016, August 7).

Determine a continuous exponential decay function and make a prediction

[Video] YouTube.

Mathispower4u. (2012, June 28).

Ex: Newton’s Law of Cooling – Exponential function app

[Video] YouTube.

Using Logistic Growth Models

Khan Academy. (2016, August 10).

Exponential and logistic growth in populations | Ecology | Khan Academy

[Video] YouTube.

Khan Academy. (2019, March 11).

Logistic growth versus exponential growth | Ecology | AP Biology | Khan Academy

[Video] YouTube.

Mathispower4u. (2011, March 30).

Logistic regression on the TI84

[Video] YouTube.

Choosing an Appropriate Model for Data

Mathispower4u. (2018, February 22).

Interpret the meaning of ordered pairs from a graph (exponential)

[Video] YouTube.

Expressing an Exponential Model in Base e

Mathispower4u. (2011, December 30).

Ex: Exponential decay function – Half life

[Video] YouTube.

Mathispower4u. (2012, June 26).

Exponential function application (y=ae^(kt)) – Bacteria growth

[Video] YouTube.

SECTION 6.8—FITTING EXPONENTIAL MODELS TO DATA

Building an Exponential Model from Data

Mathispower4u. (2012, June 28).

Ex: Perform exponential regression on a graphing calculator

[Video] YouTube.

Mathispower4u. (2020, June 17).

Perform exponential regression and make predictions using Desmos

[Video] YouTube.

Building a Logarithmic Model from Data

Mathispower4u. (2011, March 30).

Logarithmic regression on the TI84

[Video] YouTube.

resources_22sep/5.1 – 5.3 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 5

.1–5

.3

SECT

ION 5.1

—QUADRATIC FUNCTIONS

Recognizing Characteristics of Parabolas

Khan Academy. (2017, April 3).

Intro to parabolas | Khan Academy

[Video] YouTube.

Mathispower4u. (2018, December 7).

Determine key components and equation from a table of a quadratic

[Video]. YouTube.

Understanding How the Graphs of Parabolas Are Related to Their Quadratic Functions

Mathispower4u. (2011, November 30).

Ex1: Graph a quadratic function in general form

[Video]. YouTube.

Mathispower4u. (2010, July 15).

Graphing quadratic functions in standard form (vertex form)

[Video]. YouTube.

Mathispower4u. (2018, December 7).

Determine key components and graph a quadratic function y=-x^2-6x-5

[Video]. YouTube.

Mathispower4u. (2012, January 9).

Ex: Find the equation of a quadratic function from a graph

[Video]. YouTube.

Finding the Domain and Range of a Quadratic Function

Khan Academy. (2011, November 7).

Domain and range of a function given a formula | Algebra II | Khan Academy

[Video]. YouTube.

Determining the Maximum and Minimum Values of a Quadratic Function

Mathispower4u. (2015, September 25).

Ex: Quadratic function app: Maximize area of a rectangle for a given cost of fencing (vertex)

[Video]. YouTube.

Mathispower4u. (2012, June 20).

Ex: Quadratic model application – Ticket price to maximize revenue

[Video]. YouTube.

Finding the x- and y-Intercepts of a Quadratic Function

Khan Academy. (2016, March 3).

Finding features of quadratic functions | Mathematics II | High School Math | Khan Academy

[Video]. YouTube.

SECTION 5.2—POWER FUNCTIONS AND POLYNOMIAL FUNCTIONS

Identifying Power Functions:

Mathispower4u. (2019, August 6).

What are power functions? | Functions and relations, types of functions

[Video]. YouTube.

Mathispower4u. (2014, August 19).

Ex: Determine if a function is a power function

[Video]. YouTube.

Identifying End Behavior of Power Functions:

Mathispower4u. (2018, December 17).

Determine the end behavior of power functions

[Video]. YouTube.

Identifying Polynomial Functions

Polynomial Functions

Khan Academy. (2017, March 31).

Polynomials intro | Mathematics II | High School Math | Khan Academy

[Video]. YouTube.

Identifying the Degree and Leading Coefficient of a Polynomial Function

Mathispower4u. (2014, July 9).

Ex: Polynomial terminology: name, coefficient, constant, degree

[Video]. YouTube.

Identifying Local Behavior of Polynomial Functions

Fiorentino Siciliano. (2020, September 27).

Math 10 5.2 identifying local behavior of polynomial functions

[Video]. YouTube.

Intercepts and Turning Points of Polynomials

Mathispower4u. (2012, June 12).

Turning points and x intercepts of a polynomial function

[Video]. YouTube.

SECTION 5.3—GRAPHS OF POLYNOMIAL FUNCTIONS

Recognizing Characteristics of Graphs of Polynomial Functions

Mathispower4u. (2020, April 29).

Analyze a graph using desmos to determine key components of a quadratic (incr / decr / extrema)

[Video]. YouTube.

Mathispower4u. (2012, June 12).

Ex: Determine the least possible degree of a polynomial from the graph

[Video]. YouTube.

Mathispower4u. (2012, June 15).

Ex: Increasing / decreasing / relative extrema from analyzing a graph

[Video]. YouTube.

Using Factoring to Find Zeros of Polynomial Functions

Mathispower4u. (2013, January 29).

Ex: Factor and Solve a Polynomial Equation

[Video]. YouTube.

Khan Academy. (2016, February 16).

Finding zeros of polynomials (1 of 2) | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Khan Academy. (2016, February 16).

Finding zeros of polynomials (2 of 2) | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Khan Academy. (2016, February 16).

Finding zeros of polynomials (example 2) | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Identifying Zeros and Their Multiplicities

Mathispower4u. (2018, December 17).

Determine the zeros/roots and multiplicity from a graph of a polynomial

[Video]. YouTube.

Mathispower4u. (2018, December 17).

Find zeros, multiplicity, degree, and end behavior of a factored polynomial (Degree 6)

[Video]. YouTube.

Zeros of Polynomials

Mathispower4u. (2013, May 20).

Real zeros, factors, and graphs of polynomial functions

[Video]. YouTube.

Determining End Behavior

Khan Academy. (2013, December 18).

Polynomial end behavior | Polynomial and rational functions | Algebra II | Khan Academy

[Video]. YouTube.

Understanding the Relationship Between Degree and Turning Points

Fiorentino Siciliano. (2020, September 29).

Math 10 5.3 Understanding the relationship between degree and turning points

[Video]. YouTube.

Graphing Polynomial Functions

The Organic Chemistry Tutor. (2021, January 17).

How to graph polynomial functions using end behavior, multiplicity & zeros

[Video]. YouTube.

Using the Intermediate Value Theorem

Mathispower4u. (2013, June 19).

Intermediate value theorem

[Video]. YouTube.

Writing Formulas for Polynomial Functions

Mathispower4u. (2012, June 15).

Ex1: Find an equation of a degree 4 polynomial function from the graph of the function

[Video]. YouTube.

Mathispower4u. (2012, June 15).

Ex2: Find an equation of a degree 5 polynomial function from the graph of the function

[Video]. YouTube.

Using Local and Global Extrema

Fiorentino Siciliano. (2020, September 29).

Math 10 5.3 Example 11 using local extrema to solve applications

[Video]. YouTube.

resources_22sep/6.1 – 6.4 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video R

esources: Sections 6

.1

–6

.4

SECTION 6

.1

—EXPONENTIAL FUNCTIONS

Identifying Exponential Functions

Nerdstudy. (2017, February 11).

Introduction to exponential functions

[Video] YouTube.

Mathispower4u. (2014, November 29).

Introduction to exponential functions in the form f(x)=ab^x – Part 1

[Video] YouTube.

Mathispower4u. (2014, November 29).

Introduction to exponential functions in the form f(x)=ab^x – Part 2

[Video] YouTube.

Evaluating Exponential Functions

Mathispower4u. (2018, December 26).

Evaluate exponential functions: Base 3 and 1/3

[Video] YouTube.

Defining Exponential Growth

Mathispower4u. (2019, January 21).

Write exponential equations given initial values and growth or decay rate

[Video] YouTube.

Mathispower4u. (2019, January 21).

Write an exponential equation to model world population growth

[Video] YouTube.

Finding Equations of Exponential Functions

Mathispower4u. (2012, June 26).

Ex: Find an exponential growth function given two points – Initial value given

[Video] YouTube.

Mathispower4u. (2012, June 26).

Ex: Find an exponential function given two points – Initial value not given

[Video] YouTube.

Mathispower4u. (2012, June 26).

Ex: Find the equation of a transformed exponential function from a graph

[Video] YouTube.

Applying the Compound-Interest Formula

The Organic Chemistry Tutor. (2016, December 7).

Compound interest formula explained, investment, monthly & continuously, word problems, algebra

[Video] YouTube.

Mathispower4u. (2013, October 30).

Ex: Compounded interest formula – Determine deposit needed (present value)

[Video] YouTube.

Evaluating Functions with Base e

Mathispower4u. (2018, December 26).

Evaluate exponential functions: Base e

[Video] YouTube.

Investigating Continuous Growth

Mathispower4u. (2011, December 30).

Ex: Exponential growth function – Population

[Video] YouTube.

Mathispower4u. (2012, June 26).

Exponential function application (y=ae^(kt)) – Bacteria growth

[Video] YouTube.

Mathispower4u. (2016, August 7).

Determine a continuous exponential decay function and make a prediction

[Video] YouTube.

SECTION 6.2—GRAPHS OF EXPONENTIAL FUNCTIONS

Graphing Exponential Functions

Mathispower4u. (2019, October 19).

Graphing basic exponential functions: Growth and decay

[Video] YouTube.

Mathispower4u. (2016, August 7).

Graph a basic exponential function using a table of values

[Video] YouTube.

Mathispower4u. (2011, December 21).

Ex: Determine exponential graphs that have specific characteristics – y = ab^x

[Video] YouTube.

Graphing Transformations of Exponential Functions

Mathispower4u. (2012, June 22).

Ex: Match the graphs of translated exponential function to equations

[Video] YouTube.

Mathispower4u. (2013, May 15).

Ex: Equations of a transformed exponential function

[Video] YouTube.

Mathispower4u. (2015, December 21).

Ex: Determine the equation of a transformation of y=2^x

[Video] YouTube.

Mathispower4u. (2017, January 16).

Graphing exponential functions with e, transformations, domain and range, asymptotes, precalculus

[Video] YouTube.

Mathispower4u. (2012, June 26).

Ex: Find the equation of a transformed exponential function from a graph

[Video] YouTube.

SECTION 6.3—LOGARITHMIC FUNCTIONS

Converting from Logarithmic to Exponential Form

Mathispower4u. (2012, June 18).

Ex: Write logarithmic equations as exponential equations – Variables

[Video] YouTube.

Converting from Exponential to Logarithmic Form

Mathispower4u. (2011, December 23).

Ex: Write exponential equations as logarithmic equations

[Video] YouTube.

Mathispower4u. (2012, June 18).

Ex: Write exponential equations as logarithmic equations – Variables

[Video] YouTube.

Evaluating Logarithms

Mathispower4u. (2012, June 18).

Ex 1: Evaluate logarithms without a calculator – Whole numbers

[Video] YouTube.

Using Common Logarithms

Mathispower4u. (2012, June 18).

Ex: Evaluate common logarithms without a calculator

[Video] YouTube.

Mathispower4u. (2012, June 18).

Ex: Evaluate common logarithms on a calculator

[Video] YouTube.

Using Natural Logarithms:

Mathispower4u. (2011, December 23).

Ex: Evaluate natural logarithms on the calculator

[Video] YouTube.

Khan Academy. (2011, November 8).

Natural logarithm with a calculator | Logarithms | Algebra II | Khan Academy

[Video] YouTube.

SECTION 6.4—GRAPHS OF LOGARITHMIC FUNCTIONS

Finding the Domain of a Logarithmic Function

Mathispower4u. (2018, December 28).

Determine the domain, range, and asymptote of a log function y=-ln(x-6)

[Video] YouTube.

Mathispower4u. (2018, December 28).

Determine the domain, range, and asymptote of a log function y=-log_3(x)+4

[Video] YouTube.

Graphing Logarithmic Functions

Mathispower4u. (2018, December 28).

Graphing log functions by hand: y=log_(1/2)(x)

[Video] YouTube.

Mathispower4u. (2018, December 28).

Graphing logarithmic functions using Desmos.com

[Video] YouTube.

Graphing Transformations of Logarithmic Functions

Mathispower4u. (2018, December 29).

Graphing log functions by hand: y=log_3(x)+2

[Video] YouTube.

Mathispower4u. (2019, July 31).

Graphing logarithmic functions (example 1) | Algebra 2 | Khan Academy

[Video] YouTube.

Mathispower4u. (2017, January 18).

Graphing logarithmic functions with transformations, asymptotes, and domain & range

[Video] YouTube.

resources_22sep/2.4, 2.5, 2.7 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 2.4, 2.5, 2.7

SECTION 2.4—COMPLEX NUMBERS

Expressing Square Roots of Negative Numbers as Multiples of i

Mathispower4u. (2010, June 19).

Introduction to complex numbers

[Video]. YouTube.

Mathispower4u. (2016, August 5).

Simplify square roots to imaginary numbers

[Video]. YouTube.

Plotting a Complex Number on the Complex Plane

Khan Academy. (2013, August 14).

Plotting complex numbers on the complex plane | Precalculus | Khan Academy

[Video]. YouTube.

Adding and Subtracting Complex Numbers

Mathispower4u. (2016, August 5).

Write number in the form of complex numbers

[Video]. YouTube.

Investigation of Complex Numbers

Thomas Edison State University. (2022, July 5).

Investigation of Complex Numbers (kaltura.com)

[Video]. Kaltura.

Adding and Subtracting Complex Numbers

Mathispower4u. (2011, November 22).

Ex 1: Adding and subtracting complex numbers

[Video]. YouTube.

Mathispower4u. (2011, November 22).

Ex 2: Adding and subtracting complex numbers

[Video]. YouTube.

Mathispower4u. (2011, November 22).

Ex: Simplify, add, and subtract imaginary and complex numbers

[Video]. YouTube.

Multiplying Complex Numbers

Multiplying Complex Number by a Real Number

Mathispower4u. (2011, November 23).

Ex 1: Simplify and multiply complex numbers

[Video]. YouTube.

Multiplying Complex Numbers Together

Mathispower4u. (2011, November 23).

Ex 2: Multiply complex numbers

[Video]. YouTube.

Mathispower4u. (2011, November 23).

Ex 3: Multiply complex numbers

[Video]. YouTube.

Mathispower4u. (2018, April 17).

Multiply three complex numbers

[Video]. YouTube.

Mathispower4u. (2018, April 17).

Cube a complex number

[Video]. YouTube.

Mathispower4u. (2019, November 8).

Simplifying powers of i (method of dividing by 4)

[Video]. YouTube.

Mathispower4u. (2011, November 23).

Ex: Raising the imaginary unit i to powers

[Video]. YouTube.

Dividing Complex Numbers

The Complex Conjugate

Khan Academy. (2011, July 12).

Complex conjugates example | Imaginary and complex numbers | Precalculus | Khan Academy

[Video]. YouTube.

Mathispower4u. (2011, November 23).

Ex: Multiplying complex conjugates

[Video]. YouTube.

Dividing Complex Numbers

Khan Academy. (2011, July 12).

Dividing complex numbers | Imaginary and complex numbers | Precalculus | Khan Academy

[Video]. YouTube.

Mathispower4u. (2011, November 23).

Ex: Dividing complex numbers

[Video]. YouTube.

Operations of Complex Number on a Graphing Calculator

Mathispower4u. (2012, November 16).

Complex number operations on the TI-84

[Video]. YouTube.

Simplifying Powers of i

Mathispower4u. (2019, November 8).

Simplifying powers of i (method of dividing by 4)

[Video]. YouTube.

Khan Academy. (2011, July 11).

Calculating i raised to arbitrary exponents | Precalculus | Khan Academy

[Video]. YouTube.

SECTION 2.5—QUADRATIC EQUATIONS

Strategy in Factoring Quadratics

Khan Academy. (2017, April 3).

Recognizing quadratic factor methods

[Video]. YouTube.

Khan Academy. (2017, April 3).

Recognizing quadratic factor methods part 2

[Video]. YouTube.

Solving Quadratic Equations by Factoring

Zero Product Property

Mathispower4u. (2011, November 2).

The Zero-product property

[Video]. YouTube.

Solving Quadratic Equations with a Leading Coefficient of 1

Mathispower4u. (2011, October 12).

Ex: Factor and solve quadratic equations when a equals 1

[Video]. YouTube.

Mathispower4u. (2011, November 2).

Ex 1: Factor and solve quadratic equation – trinomial a = 1

[Video]. YouTube.

Solving Quadratic Equations When the Leading Coefficient is not 1

Mathispower4u. (2014, December 14).

Ex: Solve a quadratic equation using factor by grouping

[Video]. YouTube.

Mathispower4u. (2011, November 4).

Ex 1: Factor and solve a quadratic equation – a not 1

[Video]. YouTube.

Solve by Using Square Root Property

Mathispower4u. (2010, July 15).

Solving quadratic equations using square roots

[Video]. YouTube.

Mathispower4u. (2011, December 2).

Ex 1: Solving quadratic equations using square roots

[Video]. YouTube.

Mathispower4u. (2011, December 2).

Ex 2: Solving quadratic equations using square roots

[Video]. YouTube.

Completing the Square

Khan Academy. (2010, April 12).

Solving quadratic equations by completing the square | Algebra II | Khan Academy

[Video]. YouTube.

Mathispower4u. (2014, December 4).

Forming perfect square trinomials

[Video]. YouTube.

Using the Quadratic Formula

Khan Academy. (2010, April 12).

How to use the quadratic formula | Polynomial and rational functions | Algebra II | Khan Academy

[Video]. YouTube.

Mathispower4u. (2018, December 7).

Solve a quadratic equation using the quadratic formula (basic complex)

[Video]. YouTube.

Mathispower4u. (2011, December 6).

Ex1: Quadratic formula – two real irrational solutions

[Video]. YouTube.

The Discriminant

Mathispower4u. (2011, December 6).

Ex: the discriminant

[Video]. YouTube.

Khan Academy. (2011, July 12).

Discriminant for types of solutions for a quadratic | Algebra II | Khan Academy

[Video]. YouTube.

Using Pythagorean Theorem

Mathispower4u. (2010, July 15).

The Pythagorean Theorem

[Video]. YouTube.

Mathispower4u. (2011, May 24).

Example: determine the length of the hypotenuse of a right triangle

[Video]. YouTube.

Mathispower4u. (2011, May 24).

Example: determine the length of the leg of a right triangle

[Video]. YouTube.

SECTION 2.7—LINEAR INEQUALITIES AND ABSOLUTE VALUE INEQUALITIES

Using Interval Notation

Mathispower4u. (2016, May 15).

Given interval in words, graph and give interval notation

[Video]. YouTube.

Mathispower4u. (2013, May 16).

Set-Builder notation

[Video]. YouTube.

Khan Academy. (2015, June 23).

Intervals and interval notation | Functions | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2014, July 9).

Ex: Express intervals using inequalities, using a graphs, an using interval notation

[Video]. YouTube.

Using the Properties of Inequalities

Khan Academy. (2010, April 7).

Inequalities using addition and subtraction | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2011, September 26).

Ex: Solving a one step linear inequality by multiplying

[Video]. YouTube.

Solving Inequalities in One Variable Algebraically

Khan Academy. (2011, July 15).

Multi-step inequalities 3 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, January 25).

Multi-step inequalities 2 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2018, March 3).

Determine the construction steps of a two step inequality

[Video]. YouTube.

Mathispower4u. (2014, August 13).

Solving linear inequalities in one variable (l7.3)

[Video]. YouTube.

Understanding Compound Inequalities

Mathispower4u. (2014, August 13).

Introduction to basic compound inequalities – AND only (l7.5)

[Video]. YouTube.

Khan Academy. (2011, January 25).

Compound inequalities | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, January 25).

Compound inequalities 2 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, January 25).

Compound inequalities 4 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, July 15).

Compound inequalities 3 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Solving Absolute Value Inequalities

Khan Academy. (2010, April 7).

Absolute value inequalities | Linear equations | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2010, June 13).

Absolute value inequalities example 1 | Linear equations | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, January 25).

Absolute value inequalities example 2 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2010, June 13).

Absolute inequalities 2 | Linear equations | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2010, June 13).

Absolute value inequalities example 3 | Linear equations | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2010, June 13).

Writing and using inequalities | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

resources_22sep/3.5, 4.1 – 4.3 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 3

.5

, 4.1–4.3

SECTION 3.5

—TRANSFORMATION OF FUNCTIONS

Graphing Functions Using Horizontal and Vertical Shifts

Identifying Vertical Shifts

Khan Academy. (2019, July 23).

Shifting functions introduction | Transformations of functions | Algebra 2 | Khan Academy

[Video]. YouTube.

Mathispower4u. (2010, July 26).

Function transformations: Horizontal and vertical translations

[Video]. YouTube.

Identifying Horizontal Shifts:

Mathispower4u. (2010, July 26).

Function transformations: Horizontal and vertical translations

[Video]. YouTube.

Combining Horizontal and Vertical Shifts:

Mathispower4u. (2012, June 22).

Ex: Determine a function rule for a translation from a table of values

[Video]. YouTube.

Graphing Functions Using Reflections About the Axes:

Mathispower4u. (2013, May 15).

Ex: Reflect a point about the x-axis, y-axis, and the origin

[Video]. YouTube.

Mathispower4u. (2010, July 26).

Function transformations: Reflections across the x-axis and y-axis

[Video]. YouTube.

Determining Even and Odd Functions:

Mathispower4u. (2012, June 11).

Introduction to odd and even functions

[Video]. YouTube.

Mathispower4u. (2012, June 11).

Ex 2: Determine if a function is odd, even, or neither

[Video]. YouTube.

Mathispower4u. (2012, June 11).

Ex 2: Determine if a function is odd, even, or neither

[Video]. YouTube.

Vertical Stretches and Horizontal Compressions:

Mathispower4u. (2010, July 26).

Function transformations: Horizontal and vertical stretches and compressions

[Video]. YouTube.

Mathispower4u. (2013, May 15).

Determine a horizontal stretch or horizontal compression

[Video]. YouTube.

Mathispower4u. (2013, May 15).

Determine a vertical stretch or vertical compression

[Video]. YouTube.

Performing a Sequence of Transformations:

Mathispower4u. (2020, August 14).

Graph a transformation of a line segment: g(x)=-af(x+c)+d (Stretch)

[Video]. YouTube.

Mathispower4u. (2010, July 26).

Graphing multiple function transformations – Part 1 of 2

[Video]. YouTube.

Mathispower4u. (2010, July 26).

Graphing multiple function transformations – Part 2 of 2

[Video]. YouTube.

Mathispower4u. (2010, July 26).

Functions transformations: A summary

[Video]. YouTube.

SECTION 4.1—LINEAR FUNCTIONS

Representing a Linear Function in Word Form:

Khan Academy. (2010, June 12).

Recognizing linear functions | Linear equations and functions | 8th grade | Khan Academy

[Video]. YouTube.

Representing a Linear Function in Function Notation:

Mathispower4u. (2012, December 28).

Linear functions

[Video]. YouTube.

Representing a Linear Function in Tabular Form:

Mathispower4u. (2015, April 27).

Determine if a table of values represents a linear function (L9.5)

[Video]. YouTube.

Representing a Linear Function in Graphical Form:

Mathispower4u. (2017, July 10).

Linear Function as a table, graph, and equation (cell phone plan)

[Video]. YouTube.

Determining Whether a Linear Function is Increasing, Decreasing, or Constant:

Mathispower4u. (2012, December 28).

Ex: Determine if a linear function is increasing or decreasing

[Video]. YouTube.

Interpreting Slope as a Rate of Change:

Mathispower4u. (2009, September 15).

Rate and slope

[Video]. YouTube.

Mathispower4u. (2012, December 28).

Ex: Find the average rate of change – miles per hour

[Video]. YouTube.

Writing and Interpreting an Equation for a Linear Function:

Mathispower4u. (2015, April 23).

Interpreting a linear function in slope-intercept form (L10.5)

[Video]. YouTube.

Modeling Real-World Problems with Linear Functions:

Mathispower4u. (2015, April 23).

Interpreting a linear function in slope-intercept form (L10.5)

[Video]. YouTube.

Mathispower4u. (2015, October 15).

Ex: Determine the domain and range from the graph function modeling a submarine ascent

[Video]. YouTube.

Khan Academy. (2010, June 12).

Modeling with linear equations example 1 | Linear equations and functions | 8th grade | Khan Academy

[Video]. YouTube.

Graphing Linear Functions:

Mathispower4u. (2016, January 15).

Ex: Graph a linear function using a table of values (function notation)

[Video]. YouTube.

Mathispower4u. (2016, July 7).

Write and graph a linear function by making a table of values (intro)

[Video]. YouTube.

Graphing a Function Using y-intercept and Slope:

Mathispower4u. (2010, July 15).

Ex 1: Graph a linear equation in slope-intercept form

[Video]. YouTube.

The Organic Chemistry Tutor. (2018, October 3).

Ex 2: Graph a linear equation in slope-intercept form

[Video]. YouTube.

Graph a Function Using Transformations:

Mathispower4u. (2016, July 7).

Graph a linear function as a transformation of f(x)=x

[Video]. YouTube.

Mathispower4u. (2011, September 5).

Ex 1: Graph a linear equation in slope-intercept form

[Video]. YouTube.

SECTION 4.2—MODELING WITH LINEAR FUNCTIONS

Building Linear Models From Verbal Descriptions:

Mathispower4u. (2017, June 16).

Write basic expressions from words modeling situations

[Video]. YouTube.

Mathispower4u. (2014, November 26).

Ex: Determine a linear function from an application (school enrollment) (09x-36)

[Video]. YouTube.

Using a Given Intercept to Build a Model:

Mathispower4u. (2014, June 27).

Ex: Linear function population growth (parallel lines application)

[Video]. YouTube.

Using a Given Input and Output to Build a Model:

Mathispower4u. (2020, February 5).

Linear equation app: Modeling tuition cost using a linear equation

[Video]. YouTube.

Using a Diagram to Build a Model:

Mathispower4u. (2015, October 15).

Ex: Determine the domain and range from the graph function modeling a submarine ascent

[Video]. YouTube.

Modeling a Set of Data with Linear Functions:

Mathispower4u. (2015, October 18).

Ex: Model the cost of a rental truck using a linear function (m and b given)

[Video]. YouTube.

SECTION 4.3—FITTING LINEAR MODELS TO DATA

Drawing and Interpreting Scatter Plots:

Khan Academy. (2015, June 19).

Constructing a scatter plot | Regression | Probability and Statistics | Khan Academy

[Video]. YouTube.

Khan Academy. (2015, June 19).

People smoking less over time scatter plot | Regression | Probability and Statistics | Khan Academy

[Video]. YouTube.

Finding the Line of Best Fit:

Mathispower4u. (2012, December 17).

Ex: Graphical interpretation of a scatter plot and line of best fit

[Video]. YouTube.

Khan Academy. (2015, August 18).

Smoking in 1945 | Data and modeling | 8th grade | Khan Academy

[Video]. YouTube.

Finding the Line of Best Fit Using a Graphing Utility:

Mathispower4u. (2015, November 6).

Ex: Determine a Line of best fit on the TI84 and make predictions

[Video]. YouTube.

Mathispower4u. (2014, November 18).

Linear regression using Desmos

[Video]. YouTube.

Distinguishing Between Linear and Nonlinear Models:

Mathispower4u. (2011, March 28).

Introduction to regression analysis

[Video]. YouTube.

Fitting Regression Line to a Set of Data:

Khan Academy. (2018, April 24).

Introduction to inference about slope in linear regression | AP Statistics | Khan Academy

[Video]. YouTube.

Mathispower4u. (2012, October 11).

Basic linear regression example on the TI84

[Video]. YouTube.

Mathispower4u. (2014, November 18).

Linear regression using Desmos

[Video]. YouTube.

resources_22sep/DF2_ wheelchair ramp option_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Discussion Forum 2: Wheelchair Ramp Option

In this option of the activity, you will determine the length (run) of a wheelchair accessible ramp.

Read through the

U.S. Access Board

stopping after the

Rise (§405.6) portion.

For help with this option,

here is an example

to use as a reference.

You need to build a wheelchair ramp for your home for a wheelchair bound relative. Use your selected height for the ramp. The lip end of the ramp will be one quarter (¼) inch high/thick (note: this will represent your y-intercept in your drawing.) You are going to use the recommendation at the above site (“Providing the least possible slope below the 1:12 (8.33%) maximum offers better usability for a wider range of users”) and use your selected slope ratio.

Choose one height and one slope from the possible values below and post the values to the forum. You must choose a pair of values not already selected by a classmate.

Height list: 24.5; 25, 25.5 26, 26.5, 27, 27.5 28, 28.5 29, 29.5

Slope ratio: 1:12; 1:12.5; 1:13; 1:13.5; 1:14; 1:14.5; 1:15

Selected height:

Selected slope ratio:

Calculate the length (run) of the ramp, in inches, and “round” up to the next whole inch. Show the algebraic calculation.

State the length of the ramp (in inches): __________________

State the slope (ratio/fraction format), don’t forget to subtract the quarter inch lip from the original height: _________

State the ordered pair for the top of the ramp: _____________

State the equation in slope-intercept form: ________________________

State the equation in point-slope form (using the ordered pair above): ____________________

Calculate the slant distance of the ramp, show all the algebra using the distance formula.

State the slant distance, round to the nearest quarter inch: _____________________________

Place your ramp drawing with the coordinate plane in quadrant I below. Make sure your axes are labeled (

x and

y) and the axes have a proper scale.

Post your complete results (selected height and ratio, length of ramp, slope, equation, etc.) along with your drawing.

Thoroughly comment on at

least two of your classmates’ posts. Verifying their results based on the option chosen (you do not necessarily need to reply to just students who selected the same option as you. We encourage you to reply to classmates who chose a different option then you so you can get a grasp of how the content is used in both options.)

resources_22sep/2.1 – 2.3 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 2.1–2.3

SECTION 2.1

—THE RECTANGULAR COORDINATE SYSTEM AND GRAPHS

Plotting Ordered Pairs in the Cartesian Coordinate System

Khan Academy. (2012, February 15).

Introduction to the coordinate plane | Introduction to algebra | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2014, August 14).

Introduction to the cartesian plane – Part 1 (L8.1A)

[Video]. YouTube.

Mathispower4u. (2011, September 12).

Identify the quadrant of a point on the coordinate plane

[Video]. YouTube.

Graphing Equations by Plotting Points

Mathispower4u. (2009, June 10).

Graphing equations by plotting points – Part 2

[Video]. YouTube.

Mathispower4u. (2015, April 14).

Graphing by plotting points – linear (l6.3)

[Video]. YouTube.

Graphing Equations with a Graphing Utility

Mathispower4u. (2010, October 5).

Graphing lines on the TI83 or TI84

[Video]. YouTube.

Finding x-Intercepts and y-Intercepts

Khan Academy. (2015, April 21).

Introduction to intercepts | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2016, May 1).

Graph linear equations using intercepts

[Video]. YouTube.

Mathispower4u. (2018, February 22).

Interpret the meaning of the intercepts of a graph (sales and profit)

[Video]. YouTube.

Khan Academy. (2013, August 10).

Finding the x-intercept of a line | Algebra I | Khan Academy

[Video]. YouTube.

Using the Distance Formula

Mathispower4u. (2015, October 6).

Ex: Determine the distance between two points using the pythagorean theorem

[Video]. YouTube.

Mathispower4u. (2015, October 6).

Ex: Find the shortest distance between two locations north and west

[Video]. YouTube.

Using the Midpoint Formula

Mathispower4u. (2011, November 22).

Ex: Midpoint of a segment

[Video]. YouTube.

Mathispower4u. (2012, September 18).

Ex 1: Find standard equation of a circle given the endpoints of a diameter

[Video]. YouTube.

SECTION 2.2—LINEAR EQUATIONS IN ONE VARIABLE

Solving Linear Equations in One Variable

Mathispower4u. (2012, December 14).

Ex: Solving linear equations in one variable with parentheses

[Video]. YouTube.

Mathispower4u. (2014, August 12).

Solving multi-step equations (L5.4)

[Video]. YouTube.

Solving Rational Equations

Mathispower4u. (2010, July 8).

Solving rational equations

[Video]. YouTube.

Mathispower4u. (2016, June 23).

Solve basic rational equations

[Video]. YouTube.

Khan Academy. (2016, March 8).

Equations with rational expressions | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Finding a Linear Equation

Khan Academy. (2015, April 22).

Slope-intercept form | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2015, April 21).

Introduction to slope | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2016, January 15).

Ex: Determine the slope of a line given two points (horizontal and vertical)

[Video]. YouTube.

The Point Slope Formula

Khan Academy. (2013, August 5).

Introduction to point-slope form | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2011, September 9).

Ex: Find the equation of a line in point slope and slope intercept form given the slope and a point

[Video]. YouTube.

Mathispower4u. (2011, September 9).

Ex: Find the equation of the line in point-slope and slope intercept form given two points

[Video]. YouTube.

Standard Form

Khan Academy. (2015, April 22).

Standard form for linear equations | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2010, September 14).

Linear equations in standard form

[Video]. YouTube.

Mathispower4u. (2011, September 7).

Ex 1: Find the equation of a line in standard form given two points

[Video]. YouTube.

Vertical and Horizontal Lines

Mathispower4u. (2014, August 14).

Graphing horizontal and vertical lines (l8.6)

[Video]. YouTube.

Khan Academy. (2017, March 27).

Horizontal & vertical lines | Mathematics I | High School Math | Khan Academy

[Video]. YouTube.

Determining Whether Graphs of Lines Are Parallel or Perpendicular

Khan Academy. (2015, July 16).

Parallel and perpendicular lines intro | Analytic geometry | Geometry | Khan Academy

[Video]. YouTube.

Khan Academy. (2018, June 18).

Parallel & perpendicular lines from graph

[Video]. YouTube.

Writing the Equations of Lines Parallel or Perpendicular to a Given Line

Mathispower4u. (2010, September 21).

Parallel and perpendicular lines – Part 2

[Video]. YouTube.

Mathispower4u. (2016, May 1).

Determine the equation of a line perpendicular to a line in slope-intercept form

[Video]. YouTube.

SECTION 2.3—MODELS AND APPLICATIONS

Setting Up a Linear Equation to Solve a Real-World Application

Mathispower4u. (2016, January 17).

Ex: Write a linear equation that models cricket chirps (linear equation application)

[Video]. YouTube.

Mathispower4u. (2016, January 17).

Ex: Write a linear equation that models depreciation (linear equation application)

[Video]. YouTube.

Using a Formula to Solve a Real-World Application

Khan Academy. (2011, September 30).

Perimeter and area: the basics | Perimeter, area, and volume | Geometry | Khan Academy

[Video]. YouTube.

Mathispower4u. (2016, May 13).

Problem solving using distance, rate, time (running)

[Video]. YouTube.

Mathispower4u. (2011, December 6).

Ex: Find the size of cardboard needed to make a box with a given volume

[Video]. YouTube.

resources_22sep/plan for improvement_MAT-121-sep22 x

Plan for Improvement

Reflect on your past math experiences and create a plan for improvement.

1. It’s important to take the opportunity to reflect on your past experiences in math classes as you begin a new term. We can learn a lot from these reflections and work toward developing a strategy for improvement. In the table below, list 5 challenges you had in past math courses and list a possible solution that you could try this semester.

Challenge

Possible Solution

1.

2.

3.

4.

5.

2. Write your math autobiography. Tell your math story by describing your past experiences as a learner of mathematics. Share how your attitudes have changed about math over the years, if they have. Perhaps include what you like, dislike, dread, appreciate, fear, look forward to, or find beauty in. This will help your teacher to better understand you and your current feelings about the discipline.

3. Share your autobiographies with your class in Discussion Forum 1. This helps to create a community in the classroom when common themes emerge.

resources_22sep/plan for success when taking mathematics exams_MAT-121-sep22 x

Plan for Success When Taking Mathematics Exams

1. It’s important to take the opportunity to reflect on your past experiences in taking math exams as you begin a new term. We can learn a lot from these reflections and thus work toward developing a strategy for improvement.

In the table below list 5 challenges you have had in past math courses when taking an exam and list a possible solution that you could try this semester.

Challenge

Possible Solution

1.

2.

3.

4.

5.

2. Develop your plan for success. Keep in mind the idea of mindsets and try to approach your test-taking strategies with a growth mindset. Now is the time for growth as you begin a new term. Share your plan with your class in Discussion Forum 3.

resources_22sep/5.4 – 5.6 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 5.4

–5.6

SECTION 5.4

—DIVIDING POLYNOMIALS

Using Long Division to Divide Polynomials

Mathispower4u. (2009, November 5).

Polynomial division: Long division

[Video] YouTube.

Mathispower4u. (2018, December 18).

Polynomial long division: Degree 3 divided by ax+b with remainder

[Video] YouTube.

Using Synthetic Division to Divide Polynomials

Mathispower4u. (2011, October 9).

Ex 4: Divide a polynomial by a binomial using synthetic division

[Video] YouTube.

Mathispower4u. (2018, April 8).

Synthetic division: Degree 4 divided by degree 1 (missing term, neg k)

[Video] YouTube.

Using Polynomial Division to Solve Application Problems

Fiorentino Siciliano. (2020, September 30).

Math 10 5.4 Example 6 Using polynomial division in an application problem

[Video] YouTube.

SECTION 5.5—ZEROS OF POLYNOMIAL FUNCTIONS

Evaluating a Polynomial Using the Remainder Theorem

Mathispower4u. (2018, December 14).

Use the remainder theorem to determine if a binomial is a factor of a polynomial

[Video] YouTube.

Khan Academy. (2014, November 25).

Polynomial remainder theorem example | Polynomial and rational functions | Algebra II | Khan Academy

[Video] YouTube.

Khan Academy. (2014, November 25).

Polynomial remainder theorem to test factor | Algebra II | Khan Academy

[Video] YouTube.

Using the Factor Theorem to Solve a Polynomial Equation

The Organic Chemistry Tutor. (2018, February 13).

Factor theorem and synthetic division of polynomial functions

[Video] YouTube.

Using the Rational Zero Theorem to Find Rational Zeros

The Organic Chemistry Tutor. (2018, February 13).

Finding all zeros of a polynomial function using the rational zero theorem

[Video] YouTube.

Mathispower4u. (2012, April 30).

Ex 1: The zero feature of the ti84 to find rational zeros of a polynomial

[Video] YouTube.

Mathispower4u. (2012, April 30).

Ex 2: The zero feature of the ti84 to find rational zeros of a polynomial

[Video] YouTube.

Finding the Zeros of Polynomial Functions

Mathispower4u. (2012, April 20).

Ex 2: Find the zeros of a polynomial function – Real rational zeros

[Video] YouTube.

Using the Fundamental Theorem of Algebra

Khan Academy. (2014, March 26).

Fundamental theorem of algebra | Polynomial and rational functions | Algebra II | Khan Academy

[Video] YouTube.

Khan Academy. (2014, March 26).

Possible number of real roots | Polynomial and rational functions | Algebra II | Khan Academy

[Video] YouTube.

Using the Linear Factorization Theorem to Find Polynomials with Given Zeros

Mathispower4u. (2013, May 21).

Ex 1: Write a degree 3 polynomial function as a product of linear factors (2 imaginary)

[Video] YouTube.

Mathispower4u. (2013, May 21).

Ex 3: Write a degree 5 polynomial function as a product of linear factors

[Video] YouTube.

Using Descartes’ Rule of Signs

The Organic Chemistry Tutor. (2018, February 14).

Descartes rule of signs

[Video] YouTube.

Fiorentino Siciliano. (2020, October 5).

Math 10 5.5 Example 8 using Descartes’ rule of signs

[Video] YouTube.

Mario’s Math Tutoring. (2017, April 20).

How to use Descartes rule of signs example with a cubic function

[Video] YouTube.

Solving Real-World Applications

Fiorentino Siciliano. (2020, October 5).

Math 10 5.5 Example 9 solving real-world applications with polynomial equations

[Video] YouTube.

SECTION 5.6—RATIONAL FUNCTIONS

Using Arrow Notation

Fiorentino Siciliano. (2020, March 30).

Math 10 5.6 Using arrow notation/local and end behavior

[Video] YouTube.

Fiorentino Siciliano. (2020, March 30).

Math 10 5.6 Example 1: Using arrow notation

[Video] YouTube.

Khan Academy. (2016, March 11).

Graphs of rational functions: horizontal asymptote | Algebra II | High School Math | Khan Academy

[Video] YouTube.

Khan Academy. (2016, March 11).

Graphs of rational functions: horizontal asymptote | Algebra II | High School Math | Khan Academy

[Video] YouTube.

Solving Applied Problems Involving Rational Functions

Mathispower4u. (2014, July 2).

Ex: Rational function outputs and inputs application – average cost

[Video] YouTube.

Finding the Domains of Rational Functions

Mathispower4u. (2011, September 19).

Ex: Determine the domain of a rational function

[Video] YouTube.

Mathispower4u. (2011, December 9).

Ex: The domain of rational functions

[Video] YouTube.

Identifying Vertical Asymptotes of Rational Functions

The Organic Chemistry Tutor. (2017, September 9).

How to find the vertical asymptote of a function

[Video] YouTube.

Removable Discontinuities

CK-12 Foundation. (2017, June 19).

Removable discontinuities in rational functions

[Video] YouTube.

Khan Academy. (2016, March 10).

Discontinuities of rational functions | Mathematics III | High School Math | Khan Academy

[Video] YouTube.

Identifying Horizontal Asymptotes of Rational Functions

Mathispower4u. (2012, June 20).

Ex: Determine horizontal asymptotes of rational functions

[Video] YouTube.

The Organic Chemistry Tutor. (2018, January 24).

Horizontal asymptotes and slant asymptotes of rational functions

[Video] YouTube.

Intercepts of Rational Functions

Mathispower4u. (2012, June 20).

Ex: Find the intercepts and asymptotes of a rational function

[Video] YouTube.

Graphing Rational Functions

Mathispower4u. (2011, December 8).

Ex 1: Graphing rational functions

[Video] YouTube.

Mathispower4u. (2011, December 9).

Ex 6: Graphing rational functions

[Video] YouTube.

Writing Rational Functions

Mathispower4u. (2012, June 20).

Ex: Find a rational function given the vertical asymptotes and intercepts

[Video] YouTube.

Mathispower4u. (2012, June 20).

Ex 3: Find the equation of rational function from a graph

[Video] YouTube.

Mathispower4u. (2016, July 23).

Rational function application – concentration of a mixture

[Video] YouTube.

resources_22sep/Kaltura video links_MAT-121-sep22 x

Technology Activities

Geogebra overview

Technology Activity 1 instructional video for parallel lines

(TA 1 Example – Parallel lines)

Technology Activity 1 instructional video for perpendicular lines

(Technology Activity 1 Example –

Perpendicular Lines)

Desmos calculator overview

Technology Activity 2 instructional video for quadratics

(Technology Activity 2 Example – Quadratics)

Special Functions – Polynomials, Square Root, and Rational Functions

Technology Activity 2 instructional video for inequalities

(Technology Activity 2 Example – Inequalities)

Technology Activity 3 instructional video

(Technology Activity 3 Example – Linear Regression)

Technology Activity 4 instructional video

(Technology Activity 4 Example – Polynomials)

Technology Activity 5 instructional video

(Technology Activity 5 Example – Exponential Regression)

resources_22sep/1.1 – 1.3 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 1.1–1.3

SECTION 1.1—

REAL NUMBERS: ALGEBRA ESSENTIALS

Sets of Real Numbers

Mathispower4u. (2011, October 17).

Identifying sets of real numbers

[Video]. YouTube.

Determine Rational or Irrational Numbers (Square Roots and Decimals Only)

Mathispower4u. (2017, June 23).

Determine rational or irrational numbers (square roots and decimals only)

[Video]. YouTube.

Order of Operations

Mathispower4u. (2014, August 11).

Order of operations (L1.1)

[Video]. YouTube.

Properties of Real Numbers

Mathispower4u. (2016, July 1).

Properties of real numbers

[Video]. YouTube.

Evaluating Algebraic Expressions

Mathispower4u. (2011, March 30).

Evaluating algebraic expressions

[Video]. YouTube.

Circumference, Volume of a Cone, Pythagorean Theorem

Mathispower4u. (2015, April 20).

Circumference, volume of a cone, Pythagorean Theorem (L1.5)

[Video]. YouTube.

Simplifying Algebraic Expressions

Mathispower4u. (2009, August 31).

Simplifying algebraic expressions

[Video]. YouTube.

SECTION 1.2—EXPONENTS AND SCIENTIFIC NOTATION

Simplify Expressions Using the Product Rule of Exponents

Mathispower4u. (2016, July 12).

Simplify expressions using the product rule of exponents (basic)

[Video]. YouTube.

Simplify Expressions Using the Quotient Rule of Exponents

Mathispower4u. (2016, July 12).

Simplify expressions using the quotient rule of exponents (basic)

[Video]. YouTube.

Simplify Expressions Using the Power Rule of Exponents

Mathispower4u. (2016, July 12).

Simplify expressions using the power rule of exponents (basic)

[Video]. YouTube.

Evaluate and Simplify Expressions Using the Zero Exponent Rule

Mathispower4u. (2016, May 30).

Evaluate and simplify expressions using the zero exponent rule

[Video]. YouTube.

Simplify Basic Expressions with Negative Exponents

Mathispower4u. (2017, August 3).

Simplify basic expressions with negative exponents: -8^(-3), (-8)^(-3), 5y^(-1), (5y)^(-1)

[Video]. YouTube.

Simplify Expressions Using Exponent Rules (Power of a Product)

Mathispower4u. (2016, July 13).

Simplify expressions using exponent rules (power of a product)

[Video]. YouTube.

Simplify Expressions Using Exponent Rules (Power of a Quotient)

Mathispower4u. (2016, July 13).

Simplify expressions using exponent rules (power of a quotient)

[Video]. YouTube.

Simplify Exponential Expressions—Positive Exponents Only

Mathispower4u. (2011, October 1).

Ex 1: Simplify exponential expressions – Positive exponents only

[Video]. YouTube.

Scientific Notation

Mathispower4u. (2009, November 2).

Scientific notation

[Video]. YouTube.

Application of Scientific Notation—Quotient 1 (Number of Times Around the Earth)

Mathispower4u. (2016, May 31).

Application of scientific notation – quotient 1 (number of times around the earth)

[Video]. YouTube.

SECTION 1.3—RADICAL AND RATIONAL EXPONENTS

Introduction to Square Roots

Mathispower4u. (2010, November 12).

Introduction to square roots

[Video]. YouTube.

Simplifying square-root expressions

Khan Academy. (2017, March 30).

Simplifying square-root expressions | Mathematics I | High School Math | Khan Academy

[Video]. YouTube.

Adding and Subtracting Radicals

Mathispower4u. (2010, July 9).

Adding and subtracting radicals

[Video]. YouTube.

Rationalize the Denominator—Square Root with Variable

Mathispower4u. (2018, April 17).

Rationalize the denominator – square root with variable

[Video]. YouTube.

Rationalize the Denominator of a Radical Expression—Conjugate

Mathispower4u. (2011, November 18).

Ex: rationalize the denominator of a radical expression – conjugate

[Video]. YouTube.

Simplify Nth Roots with Variables

Mathispower4u. (2016, August 4).

Simplify nth roots with variables

[Video]. YouTube.

Write Rational Exponents as Radicals and Radicals Using Rational Exponents (Variables)

Mathispower4u. (2018, April 14).

Write rational exponents as radicals and radicals using rational exponents (variables)

[Video]. YouTube.

Simplify Expressions with Rational Exponents

Mathispower4u. (2011, November 16).

Ex: Simplify expressions with rational exponents

[Video]. YouTube.

resources_22sep/study skills survey_MAT-121-sep22 x

Behavior or Belief

Always

Sometimes

Never

1. Contact my instructor if I must miss logging in for a few days. Review announcements posted by my instructor when I finally log in.

2. Read through assigned textbook readings before beginning my homework.

3. Connect with a study partner/friend either locally or virtually.

4. Spend time on homework each day.

5. Begin to review for exams at least a week prior to exam.

6. Use the exam practice test and take it before an exam.

7. Find my instructor’s office hours and stop in virtually for help or schedule a help session if I am unable to attend the weekly office hour.

8. Locate the math tutoring resources for students (on campus) and make note of available hours.

9. Visit math tutoring services for assistance on a regular basis (virtually).

10. Spend at least two hours studying outside of class for each hour in class (virtually).

11. Check my progress in my math course through my college’s learning management system (LMS) gradebook.

12. Scan through my entire test before beginning and start off working on a problem I am confident in solving.

13. Gain access to the Moodle course website by the end of the first week of classes.

14. Send a message, through the course mechanisms, to my instructor when I need assistance.

15. Create a schedule for each week including assignment due dates, reading, and study time.

16. Feel confident when I start a math exam.

17. Keep a separate notebook for each class I am taking. Divide math notebooks or binders into separate sections for homework and notes.

18. Talk honestly about classes with a friend or family member on a regular basis.

19. Add test dates to a calendar at the beginning of the semester.

20. Take notes for each textbook reading section.

21. Ask my instructor questions either during office hours or posted in the course (virtually) if I don’t understand.

22. Complete module homework assignments.

23. Engage in class discussions (virtually).

24. Have a quiet and organized place to study.

25. Avoid calls or texts from friends when I’m studying.

26. Set study goals for myself each week.

27. Think about my academic major and future occupation.

28. Take responsibility for my study plan.

29. Try different approaches to solve a problem when I get stuck.

30. Believe that I can be successful in any college math course.

31. Search for instructional videos online, or posted in the course and/or book, when I get really stuck on a section or an exercise.

32. Create flashcards to help in memorizing important formulas and strategies.

Total number in each column:

Scoring:

Always:

4 points each

Sometimes:

2 points each

Never:

0 points each

Total Points:

Practice Makes Perfect

Identify the study skills leading to success in a college-level mathematics course.

.

1. Each of the behaviors or attitudes listed in the table above are associated with success in college mathematics. This means that students who use these strategies or are open to these beliefs are successful learners. Share your total score with your class in Discussion Forum 1 and be supportive of your fellow students!

2. Based on this survey, create a list of the top 5 strategies that you currently utilize and feel are most helpful to you.

1.

2.

3.

4.

5.

3. Based on this survey, create a list of the top 5 strategies that interest you and that you feel could be most helpful to you this term. Plan on implementing these strategies.

1.

2.

3.

4.

5.

resources_22sep/DF2_ wheelchair ramp example_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Discussion Forum 2: Wheelchair Ramp Example

You need to build a wheelchair ramp for your home for a wheelchair bound relative. Use your selected height for the ramp. We will use the height of 30” which is the maximum height for a single run wheelchair ramp. The lip end of the ramp will be one quarter (¼) inch high/thick (note: this will represent your

y-intercept in your drawing.) You are going to use the recommendation at the ADA site (“Providing the least possible slope below the 1:12 (8.33%) maximum offers better usability for a wider range of users”) and use your selected slope ratio. We will use the 1:12 slope ratio.

Calculate the length (run) of the ramp, in inches, and “round” up to the next whole inch. Show the algebraic calculation.

We can use equal ratios to determine the length (run) of the ramp: , where

x represents the length of the run in inches: Since we are working with equal ratios we can use the technique of cross multiplying to solve for

x. Another way to write our equal ratios is: (if 2 ratios are equal then their reciprocals are equal also.) This makes the cross multiplication easier to solve for

x in a single step. Cross multiplying we have: . So we see that the run needs to be 360”

State the length of the ramp (in inches): _____

360”_____________

State the slope (ratio/fraction format), don’t forget to subtract the quarter inch lip from the original height: _________

(You may wonder why our slope isn’t 1/12 which is the slope ratio 1:12 that we used. This is because we have the quarter inch lip at the beginning of the ramp. So if we use the slope formula to calculate the slope we get: after dividing numerator and denominator by the GCF (25). If you convert the 1:12 slope ratio to decimal value and our slope ratio to a decimal you will see that which is less than . So our slope ratio is within the ADA requirement guidelines. This may be a little confusing, but it gives you an idea of how real-world mathematics may be slightly different then “book” mathematics.)

State the ordered pair for the top of the ramp: ____

(360, 30)_________

State the equation in slope-intercept form: ________________________

State the equation in point-slope form (using the ordered pair above): ____________________

Calculate the slant distance of the ramp, show all the algebra using the distance formula.

Distance:

State the slant distance, round to the nearest quarter inch: ____________________

Place your ramp drawing with the coordinate plane in quadrant I below. Make sure your axes are labeled (

x and

y) and the axes have a proper scale.

Because of the 1:12 ratio for the slope the ramp looks taller than what it would be in real life (notice the axes have different scales.)

image1

image2

resources_22sep/mathematics exam study skills survey_MAT-121-sep22 x

Exam Preparation Strategies

Always

Sometimes

Never

1. Rework each of the examples my instructor posted online and the problems in any assignment.

2. Create note cards to help in memorizing important formulas and problem solving strategies for the exam.

3. Create a study schedule for each math exam and begin to study for the exam at least one week prior to the date. Spaced practice over 5 to 7 days is much more effective than cramming material in 1 to 2 sessions.

4. Work the review exercises at the end of each chapter of the text.

5. Visit my instructor’s office hours when I need assistance in preparing for an exam or schedule a help session if I cannot attend the weekly mentor office hour.

6. Spend time on note interactions (see the document on Cornell notes) each day.

7. Take the practice test online posted in the course and take it the week before the exam.

8. Review each of the student learning objectives at the beginning of all sections covered on the exam and use this list as a checklist for exam preparation.

9. Refer to the syllabus about how many questions will be on the exam and if they award partial credit.

10. Work through the practice test at the end of each chapter of the text.

11. Get a good night’s sleep the night before my exam.

12. Come to each exam prepared with a goal of earning an A.

13. Make sure to grab a healthy breakfast the day of the exam.

14. Log in early to class on exam days. Review requirements for taking exams online through Proctor U.

15. Keep my phone put away in my bag during exams to avoid distractions.

16. Try to relax and take a few deep breaths before beginning the exam.

17. Use a pencil so that I can make corrections neatly on my worksheet.

18. Read through all directions before beginning the exam.

19. Write formulas that are memorized in the margins of my worksheet to reference when/if needed.

20. Scan through my entire test before beginning and start off working on a problem I am confident in solving.

21. Work each of the questions that I find easier first.

22. Keep track of time. Do a quick assessment of how much time should be spent on each question.

23. Try different approaches to solve problems when I get stuck.

24. Draw a diagram when solving an application problem.

25. Do some work on each question.

26. Work neatly and show all steps.

27. Make sure to attach units to final answers when units are given in the problem (for example: cm, $, or feet/second).

28. Stay working for the entire online exam session. If finished early I will use the additional time to review my work and check answers.

29. Select the final answer for each question/problem.

30. Make sure I know how to use all the necessary functionality of my scientific/graphing calculator that I will need during the exam.

After the Exam Behaviors and Strategies

Always

Sometimes

Never

31. Take responsibility for my exam performance and try to learn from the experience.

32. Reflect on the test-taking experience and make a list for myself on what to do differently next time.

33. Reflect on my feelings while taking the exam. Plan to replace any negative self-statements with positive ones on future exams.

34. Celebrate my success after doing well on an exam! Talk to a friend or family member about my progress.

Total Number in Each Column:

Scoring:

Always:

4 points each

Sometimes:

2 points each

Never:

0 points each

Total Points:

Practice Makes Perfect

Identify the study skills leading to successful preparation for a college-level mathematics exam.

1. Each of the behaviors or attitudes listed in the table above are associated with successful college mathematics exam preparation. This means that students who use these strategies or are open to these beliefs pass their college math courses. Compute your total score and share your score with your class in Discussion Forum 3. Be supportive of your fellow students and offer encouragement!

Total score =__________

2. Based on this survey, create a list of the top 5 test-preparation and test-taking strategies that you currently utilize and feel are most helpful to you.

1.

2.

3.

4.

5.

3. Based on this survey, create a list of the top 5 test-preparation and test-taking strategies that interest you and that you feel could be most helpful to you this term. Plan on implementing these strategies.

1.

2.

3.

4.

5.

resources_22sep/3.1 – 3.4 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 3

.1–3.4

SECTION 3

.1

—FUNCTIONS AND FUNCTION NOTATION

Determining Whether a Relation Represents a Function

Mathispower4u. (2014, August 14).

Introduction to relations and functions (L9.1)

[Video]. YouTube.

Using Function Notation

Mathispower4u. (2014, August 14).

Introduction to function notation (L9.2)

[Video]. YouTube.

Mathispower4u. (2018, February 24).

Application: Determine the meaning of function values

[Video]. YouTube.

Representing Functions Using Tables

Mathispower4u. (2015, November 27).

Ex: Use a table to find function inputs and outputs – items sold application

[Video]. YouTube.

Mathispower4u. (2019, May 16).

Represent a discrete function using ordered pairs, a table, and function notation

[Video]. YouTube.

Finding Input and Output Values of a Function

Evaluation of Functions in Algebraic Forms

Khan Academy. (2013, June 4).

Evaluating functions given their formula | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Mathispower4u. (2014, August 14).

Evaluating functions using function notation (l9.3)

[Video]. YouTube.

Mathispower4u. (2018, February 24).

Determine a variety of function values

[Video]. YouTube.

Evaluating Functions Expressed in Formulas

Mathispower4u. (2013, July 15).

Ex: Find an output of a demand function

[Video]. YouTube.

Khan Academy. (2015, August 6).

How to interpret an expression with function notation | Functions | Algebra I | Khan Academy

[Video]. YouTube.

Evaluating Functions Given in Tabular Form

Mathispower4u. (2012, June 7).

Ex: Evaluate a function and solve for a function value given a table

[Video]. YouTube.

Finding Function Values From a Graph

Mathispower4u. (2011, October 17).

Ex: Given a graph and a function value, determine the input or x-value

[Video]. YouTube.

Khan Academy. (2013, June 4).

Evaluating functions given their graph | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Determining Whether a Function is One-to-One

Mathispower4u. (2012, June 6).

Determine if a relation given as a table is a one-to-one function

[Video]. YouTube.

Using the Vertical Line Test

Mathispower4u. (2012, June 6).

Ex 1: Determine if the graph of a relation is a one-to-one function

[Video]. YouTube.

Using the Horizontal Line Test

Mathispower4u. (2012, June 6).

Ex 1: Determine if the graph of a relation is a one-to-one function

[Video]. YouTube.

Mathispower4u. (2012, June 6).

Ex 2: Determine if the graph of a relation is a one-to-one function

[Video]. YouTube.

Mathispower4u. (2018, February 11).

Horizontal line test and one to one functions

[Video]. YouTube.

Identifying Basic Toolkit Functions

Mathispower4u. (2013, May 6).

Graphing 9 basic functions

[Video]. YouTube.

SECTION 3.2—DOMAIN AND RANGE

Restrictions on the Domain and Range

The Organic Chemistry Tutor. (2017, September 8).

How to find the domain of a function – Radicals, fractions & square roots – Interval notation

[Video]. YouTube.

Finding the Domain of a Function Defined by an Equation

Interval Notation

Khan Academy. (2015, June 23).

Intervals and interval notation | Functions | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2015, October 13).

Ex 1: Find domain and range of ordered pairs, function or not

[Video]. YouTube.

Mathispower4u. (2011, September 19).

Ex: Determine the domain of a rational function

[Video]. YouTube.

Using Notations to Specify Domain and Range

The Organic Chemistry Tutor. (2018, February 7).

Set builder notation and roster method

[Video]. YouTube.

Mathispower4u. (2014, August 13).

Introduction to basic inequalities in one variable (L7.2)

[Video]. YouTube.

Finding Domain and Range From Graphs

Mathispower4u. (2019, May 16).

Determine the domain and range from a graph: semicircle

[Video]. YouTube.

Mathispower4u. (2013, May 29).

Ex: Give the domain and range given the graph of a function

[Video]. YouTube.

Finding the Domains and Ranges of the Toolkit Functions

Mathispower4u. (2014, August 13).

Introduction to basic inequalities in one variable (L7.2)

[Video]. YouTube.

Graphing Piecewise-Defined Functions

Piecewise Functions

Khan Academy. (2015, March 5).

Piecewise function formula from graph | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Mathispower4u. (2016, July 8).

Determine a basic piecewise defined function

[Video]. YouTube.

Khan Academy. (2015, March 5).

Graphing piecewise function | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

SECTION 3.3—RATES OF CHANGE AND BEHAVIOR OF GRAPHS

Finding Average Rate of Change of a Function

Mathispower4u. (2012, June 14).

Ex: Find the average rate of change from a table – Temperatures

[Video]. YouTube.

Mathispower4u. (2012, June 14).

Ex: Find the average rate of change given a function rule

[Video]. YouTube.

Mathispower4u. (2012, June 14).

Ex: Find the average rate of change from a graph

[Video]. YouTube.

Using a Graph to Determine Where a Function is Increasing, Decreasing, or Constant

Mathispower4u. (2013, June 25).

Ex: Determine if a function is incr, decr, or constant from graph, table, and ordered pairs

[Video]. YouTube.

Mathispower4u. (2012, June 15).

Ex: Increasing / decreasing / relative extrema from analyzing a graph

[Video]. YouTube.

Mathispower4u. (2012, June 15).

Ex: Increasing / decreasing / relative extrema from analyzing a graph

[Video]. YouTube.

Analyzing the Toolkit Functions for Increasing or Decreasing Intervals

Fiorentino Siciliano. (2020, September 2).

Math 10 3.3. Analyzing the toolkit functions for increasing or decreasing intervals

[Video]. YouTube.

Using a Graph to Locate the Absolute Maximum and Absolute Minimum

Khan Academy. (2014, January 20).

Introduction to minimum and maximum points | Functions | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2018, January 4).

How to recognize relative and absolute maxima and minima | Functions | Algebra I | Khan Academy

[Video]. YouTube.

SECTION 3.4—COMPOSITION OF FUNCTIONS

Combining Functions Using Algebraic Operations

Khan Academy. (2011, November 7).

Sum of functions | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, November 7).

Sum of functions | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, November 7).

Product of functions | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, November 7).

Quotient of functions | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Create a Function by Composition of Functions

Khan Academy. (2014, March 28).

Introduction to function composition | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Evaluating Composite Functions

Evaluating Composite Functions Using Tables

Khan Academy. (2016, February 12).

Evaluating composite functions: using tables | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Evaluating Composite Functions Using Graphs

Khan Academy. (2016, February 12).

Evaluating composite functions: using graphs | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Evaluating Composite Functions Using Formulas

Khan Academy. (2016, March 4).

Evaluating composite functions | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Mathispower4u. (2011, December 19).

Ex 1: Composite Function Values

[Video]. YouTube.

Mathispower4u. (2012, June 11).

Ex: Find and Evaluate a Composition of Three Functions

[Video]. YouTube.

Mathispower4u. (2014, June 25).

Ex: Evaluate Functions and Composite Function in Context of a Story (Graphing Calculator)

[Video]. YouTube.

Finding the Domain of Composite Function

Mathispower4u. (2021, September 11).

Composition of Two Function and the Domain

[Video]. YouTube.

Mathispower4u. (2021, September 11).

Composition of Three Function and the Domain

[Video]. YouTube.

Mathispower4u. (2011, December 19).

Ex 3: Domain of a Composite Function

[Video]. YouTube.

Mathispower4u. (2011, December 19).

Ex 4: Domain of a Composite Function

[Video]. YouTube.

Decomposing a Composite Function into Its Component Functions

Mathispower4u. (2012, June 11).

Ex: Decompose Functions

[Video]. YouTube.

technology activities_22sep/Technology Activity 3 Data sets/Malignant Neoplasms.xlsx

Sheet1

Malignant Neoplasms

Year

t

Number of Deaths – Male

Number of Deaths – Female

1950

0

208.1

182.3

1960

10

225.1

168.7

1970

20

247.6

163.2

1980

30

271.2

166.7

1981

31

268.6

166.2

1982

32

271.9

166.7

1983

33

272.9

168.5

1984

34

273.8

170.8

1985

35

274.4

171.2

1986

36

274.5

171.7

1987

37

274.8

171.7

1988

38

275.5

172.7

1989

39

277.1

174.4

1990

40

280.4

175.7

1991

41

278.2

175.7

1992

42

275.6

174.7

1993

43

274.9

174.9

1994

44

271.1

174.4

1995

45

267.5

173.6

1996

46

262.4

171.3

1997

47

257

169.3

1998

48

252.6

167.2

1999

49

251.9

167.6

2000

50

248.9

167.6

2001

51

244.5

165.1

2002

52

240.9

163.7

2003

53

235.1

161.5

2004

54

229.5

158.2

2005

55

227.2

156.7

2006

56

221.7

154.7

2007

57

218.8

152.3

2008

58

214.9

149.6

2009

59

210.9

147.4

2010

60

209.9

146.7

2011

61

204

144

2012

62

200.3

142.1

2013

63

196

139.5

2014

64

192.9

138.1

2015

65

189.2

135.9

2016

66

185.4

134

2017

67

181.1

131.4

2018

68

176.8

128.6

2017

42

6.63

2.9

2018

43

6.18

2.81

technology activities_22sep/Technology Activity 3 Data sets/Non-Hodgkin Lymphoma.xlsx

Sheet1

Non-Hodgkin Lymphoma

Year

t

New Cases

Death Rate

1975

0

11.06

5.63

1976

1

11.22

5.71

1977

2

11.18

5.77

1978

3

11.92

5.93

1979

4

12.53

5.95

1980

5

12.62

6.23

1981

6

13.58

6.16

1982

7

13.39

6.55

1983

8

13.99

6.66

1984

9

15.19

6.76

1985

10

15.51

7.06

1986

11

15.9

7.31

1987

12

16.74

7.26

1988

13

17.26

7.52

1989

14

17.36

7.83

1990

15

18.51

7.87

1991

16

18.81

8.19

1992

17

18.63

8.22

1993

18

18.86

8.25

1994

19

19.94

8.63

1995

20

20.01

8.72

1996

21

19.42

8.75

1997

22

20

8.88

1998

23

19.62

8.69

1999

24

19.98

8.32

2000

25

19.82

8.17

2001

26

20.02

7.91

2002

27

20.23

7.65

2003

28

20.8

7.38

2004

29

21.41

7.09

2005

30

20.9

6.95

2006

31

20.51

6.74

2007

32

21.3

6.59

2008

33

20.95

6.41

2009

34

20.9

6.3

2010

35

21.41

6.14

2011

36

19.78

6.03

2012

37

20.32

5.91

2013

38

19.81

5.71

2014

39

20.3

5.66

2015

40

20.15

5.48

2016

41

19.62

5.38

2017

42

19.43

5.31

2018

43

19.06

5.13

technology activities_22sep/Technology Activity 3 Data sets/Cerebrovascular Diseases.xlsx

Sheet1

Cerebrovascular Diseases

Year

t

Number of Deaths – Male

Number of Deaths – Female

1950

0

186.4

175.8

1960

10

186.1

170.7

1970

20

157.4

140

1980

30

102.2

91.7

1981

31

94.4

85.7

1982

32

89

80.4

1983

33

86

77.4

1984

34

82.9

75.4

1985

35

79.9

73.3

1986

36

76.4

70.2

1987

37

74.8

68.8

1988

38

74.5

67.4

1989

39

70.2

64.1

1990

40

68.5

62.6

1991

41

66.4

60

1992

42

64.9

58.7

1993

43

66.3

59.8

1994

44

65.9

59.8

1995

45

65.9

60.5

1996

46

65.3

59.9

1997

47

63.9

58.6

1998

48

60.7

57.6

1999

49

63.2

59.8

2000

50

62.4

59.1

2001

51

59.5

56.8

2002

52

57.9

56.1

2003

53

55.4

53.2

2004

54

51.7

50.2

2005

55

48.4

47

2006

56

45.2

43.9

2007

57

43.7

42.7

2008

58

42.2

41.4

2009

59

39.9

38.8

2010

60

39.3

38.3

2011

61

37.9

37.2

2012

62

37.1

36.1

2013

63

36.7

35.2

2014

64

36.9

35.6

2015

65

37.8

36.9

2016

66

37.5

36.5

2017

67

38

36.6

2018

68

37.6

36.1

2017

42

6.63

2.9

2018

43

6.18

2.81

technology activities_22sep/Technology Activity 3 Data sets/Soft Tissue including Heart Cancer.xlsx

Sheet1

Soft Tissue including Heart Cancer

Year

t

New Cases

Death Rate

1975

0

2.21

0.9

1976

1

2.23

0.86

1977

2

2.26

0.92

1978

3

2.47

0.94

1979

4

2.23

1.23

1980

5

2.1

1.22

1981

6

2.14

1.26

1982

7

2.31

1.23

1983

8

2.35

1.26

1984

9

2.46

1.28

1985

10

2.27

1.33

1986

11

2.32

1.29

1987

12

2.46

1.35

1988

13

2.43

1.32

1989

14

2.32

1.31

1990

15

2.49

1.36

1991

16

2.64

1.39

1992

17

2.58

1.41

1993

18

2.53

1.49

1994

19

2.68

1.49

1995

20

2.85

1.5

1996

21

2.83

1.5

1997

22

3

1.55

1998

23

2.88

1.49

1999

24

2.9

1.34

2000

25

3.01

1.32

2001

26

3.12

1.29

2002

27

3

1.24

2003

28

3.09

1.25

2004

29

3.23

1.25

2005

30

3.37

1.27

2006

31

3.08

1.29

2007

32

3.41

1.29

2008

33

3.4

1.29

2009

34

3.38

1.3

2010

35

3.35

1.33

2011

36

3.29

1.31

2012

37

3.47

1.33

2013

38

3.44

1.31

2014

39

3.48

1.34

2015

40

3.46

1.32

2016

41

3.51

1.31

2017

42

3.46

1.33

2018

43

3.12

1.32

technology activities_22sep/Technology Activity 3 Data sets/Thyroid Cancer.xlsx

Sheet1

Thyroid Cancer

Year

t

New Cases

Death Rate

1975

0

4.85

0.55

1976

1

4.78

0.56

1977

2

5.44

0.57

1978

3

5.1

0.55

1979

4

4.48

0.53

1980

5

4.33

0.48

1981

6

4.42

0.5

1982

7

4.63

0.48

1983

8

4.72

0.44

1984

9

4.85

0.47

1985

10

5.13

0.45

1986

11

5.32

0.46

1987

12

5.04

0.45

1988

13

4.93

0.44

1989

14

5.37

0.44

1990

15

5.5

0.44

1991

16

5.49

0.43

1992

17

5.88

0.46

1993

18

5.65

0.46

1994

19

6.09

0.42

1995

20

6.23

0.44

1996

21

6.54

0.45

1997

22

6.79

0.46

1998

23

6.99

0.44

1999

24

7.35

0.45

2000

25

7.62

0.48

2001

26

8.31

0.48

2002

27

9.24

0.48

2003

28

9.67

0.45

2004

29

10.15

0.48

2005

30

10.97

0.48

2006

31

11.33

0.49

2007

32

12.31

0.5

2008

33

13.21

0.52

2009

34

14.49

0.52

2010

35

13.98

0.51

2011

36

14.8

0.51

2012

37

15

0.48

2013

38

15.18

0.52

2014

39

15.17

0.5

2015

40

15.11

0.51

2016

41

14.6

0.54

2017

42

13.77

0.49

2018

43

13.46

0.51

technology activities_22sep/Technology Activity 3 Data sets/Melanoma of the Skin.xlsx

Sheet1

Melanoma of the Skin

Year

t

New Cases

Death Rate

1975

0

7.89

2.07

1976

1

8.15

2.24

1977

2

8.87

2.27

1978

3

8.95

2.31

1979

4

9.53

2.42

1980

5

10.51

2.34

1981

6

11.09

2.43

1982

7

11.19

2.46

1983

8

11.08

2.48

1984

9

11.41

2.53

1985

10

12.78

2.56

1986

11

13.32

2.59

1987

12

13.68

2.65

1988

13

12.89

2.65

1989

14

13.75

2.69

1990

15

13.88

2.75

1991

16

14.63

2.71

1992

17

14.77

2.71

1993

18

14.65

2.71

1994

19

15.67

2.66

1995

20

16.5

2.7

1996

21

17.4

2.8

1997

22

17.78

2.73

1998

23

17.97

2.75

1999

24

18.38

2.63

2000

25

19.01

2.66

2001

26

19.75

2.66

2002

27

19.38

2.61

2003

28

19.6

2.67

2004

29

20.73

2.67

2005

30

22.52

2.76

2006

31

22.2

2.74

2007

32

21.89

2.68

2008

33

23.29

2.69

2009

34

23.24

2.81

2010

35

23.96

2.74

2011

36

23.01

2.69

2012

37

23.1

2.66

2013

38

24.25

2.67

2014

39

25.48

2.57

2015

40

25.93

2.41

2016

41

25.79

2.17

2017

42

25.62

2.09

2018

43

25.32

2.08

technology activities_22sep/Technology Activity 3 Data sets/Bladder Cancer.xlsx

Sheet1

Bladder Cancer

Year

t

New Cases

Death Rate

1975

0

19.31

5.5

1976

1

19.69

5.59

1977

2

18.99

5.52

1978

3

19.99

5.44

1979

4

19.98

5.25

1980

5

20.42

5.17

1981

6

20.69

5.07

1982

7

20.09

4.99

1983

8

20.04

4.88

1984

9

20.85

4.74

1985

10

20.68

4.67

1986

11

21.02

4.53

1987

12

21.66

4.41

1988

13

20.85

4.41

1989

14

21.03

4.48

1990

15

21.08

4.49

1991

16

20.92

4.42

1992

17

21.26

4.46

1993

18

21.27

4.47

1994

19

20.81

4.47

1995

20

20.64

4.35

1996

21

20.83

4.41

1997

22

21.11

4.39

1998

23

21.63

4.38

1999

24

21.78

4.36

2000

25

21.86

4.32

2001

26

21.8

4.35

2002

27

21.29

4.43

2003

28

21.62

4.3

2004

29

21.59

4.42

2005

30

22.02

4.42

2006

31

21.43

4.41

2007

32

21.96

4.44

2008

33

21.44

4.41

2009

34

20.95

4.37

2010

35

21.41

4.43

2011

36

20.45

4.43

2012

37

20.82

4.38

2013

38

20.15

4.44

2014

39

20.47

4.35

2015

40

20.05

4.37

2016

41

19.69

4.38

2017

42

19.17

4.27

2018

43

18.2

4.16

technology activities_22sep/Technology Activity 3 Data sets/Ovarian Cancer.xlsx

Sheet1

Ovarian Cancer

Year

t

New Cases

Death Rate

1975

0

16.32

9.84

1976

1

15.84

10.02

1977

2

2.68

2.78

1978

3

2.67

2.74

1979

4

15.4

9.33

1980

5

15.46

9.29

1981

6

15.43

9.23

1982

7

15.59

9.22

1983

8

15.97

9.2

1984

9

16.26

9.11

1985

10

16.56

9.08

1986

11

15.01

9.24

1987

12

16.15

9.18

1988

13

15.28

9.31

1989

14

15.53

9.21

1990

15

15.39

9.33

1991

16

15.79

9.51

1992

17

14.94

9.46

1993

18

15.26

9.08

1994

19

14.49

9.38

1995

20

14.6

9.12

1996

21

14.13

8.86

1997

22

14.73

8.94

1998

23

14.36

8.73

1999

24

14.73

8.77

2000

25

14.37

8.89

2001

26

14.62

9

2002

27

13.9

9.04

2003

28

13.74

8.87

2004

29

13.38

8.78

2005

30

13.02

8.66

2006

31

13.02

8.56

2007

32

13.04

8.25

2008

33

12.99

7.98

2009

34

13.09

7.85

2010

35

12.88

7.8

2011

36

12.4

7.54

2012

37

12.11

7.4

2013

38

11.64

7.21

2014

39

11.66

7.03

2015

40

11.7

6.75

2016

41

10.32

6.77

2017

42

10.36

6.59

2018

43

9.25

6.28

technology activities_22sep/Technology Activity 3 Data sets/Heart Disease.xlsx

Sheet1

Heart Disease

Year

t

Number of Deaths – Male

Number of Deaths – Female

1950

0

699

486.6

1960

10

687.6

447

1970

20

634

381.6

1980

30

538.9

320.8

1981

31

520.9

308.1

1982

32

509.6

302.8

1983

33

507.9

304.1

1984

34

493.5

297.2

1985

35

488

294.5

1986

36

470.7

289.3

1987

37

456.9

283.4

1988

38

451.8

281.5

1989

39

424.4

265.5

1990

40

412.4

257

1991

41

400.1

249.7

1992

42

389

243

1993

43

392.1

247.5

1994

44

377.6

239.3

1995

45

371

236.6

1996

46

360.7

230.8

1997

47

349.5

224.6

1998

48

339.3

220.7

1999

49

331

218.1

2000

50

320

210.9

2001

51

307.8

205.4

2002

52

303.4

200.3

2003

53

292.3

193.7

2004

54

274.1

181.5

2005

55

268.2

177.5

2006

56

254.9

167.2

2007

57

243.7

159

2008

58

238.5

155.9

2009

59

229.4

146.6

2010

60

225.1

143.3

2011

61

218.1

138.7

2012

62

214.7

135.5

2013

63

214.5

134.3

2014

64

210.9

131.8

2015

65

211.8

133.6

2016

66

209.1

130.4

2017

67

209

129.6

2018

68

207.5

127.9

technology activities_22sep/Technology Activity 3 Data sets/Kidney and Renal Pelvis Cancer.xlsx

Sheet1

Kidney and Renal Pelvis Cancer

Year

t

New Cases

Death Rate

1975

0

7.08

3.61

1976

1

7.97

3.61

1977

2

8.06

3.68

1978

3

7.85

3.69

1979

4

7.63

3.63

1980

5

8.06

3.68

1981

6

8.49

3.73

1982

7

8.35

3.85

1983

8

8.94

3.85

1984

9

9.19

3.9

1985

10

8.94

3.96

1986

11

9.65

4.05

1987

12

9.9

4.14

1988

13

9.94

4.03

1989

14

10.32

4.16

1990

15

10.44

4.19

1991

16

10.65

4.3

1992

17

10.81

4.29

1993

18

10.76

4.16

1994

19

11.3

4.27

1995

20

11.12

4.34

1996

21

11.36

4.27

1997

22

10.97

4.27

1998

23

11.82

4.26

1999

24

11.46

4.06

2000

25

12.53

4.22

2001

26

12.62

4.27

2002

27

12.94

4.23

2003

28

13.57

4.2

2004

29

13.66

4.13

2005

30

14.08

4.13

2006

31

14.72

4

2007

32

15.62

4.02

2008

33

16.02

3.99

2009

34

15.4

3.93

2010

35

15.02

3.92

2011

36

15.58

3.94

2012

37

15.69

3.83

2013

38

15.64

3.86

2014

39

15.57

3.76

2015

40

16.06

3.82

2016

41

15.89

3.6

2017

42

15.83

3.55

2018

43

15.63

3.52

technology activities_22sep/Technology Activity 3 Data sets/Testicular Cancer.xlsx

Sheet1

Testicular Cancer

Year

t

New Cases

Death Rate

1975

0

3.73

0.74

1976

1

3.44

0.71

1977

2

4.3

0.65

1978

3

3.59

0.56

1979

4

3.89

0.52

1980

5

4.34

0.45

1981

6

4.23

0.37

1982

7

4.4

0.4

1983

8

4.6

0.39

1984

9

4.4

0.35

1985

10

4.47

0.36

1986

11

4.81

0.32

1987

12

5.05

0.34

1988

13

4.63

0.32

1989

14

5.48

0.32

1990

15

5.1

0.27

1991

16

5.1

0.29

1992

17

5.15

0.28

1993

18

5.07

0.3

1994

19

5.49

0.27

1995

20

4.55

0.24

1996

21

5.25

0.26

1997

22

5.43

0.24

1998

23

5.6

0.28

1999

24

5.45

0.28

2000

25

5.75

0.25

2001

26

5.54

0.24

2002

27

5.8

0.28

2003

28

5.36

0.25

2004

29

5.99

0.25

2005

30

6.04

0.25

2006

31

5.68

0.25

2007

32

6.03

0.22

2008

33

6.08

0.24

2009

34

5.88

0.25

2010

35

5.88

0.26

2011

36

5.95

0.25

2012

37

5.99

0.25

2013

38

6.1

0.24

2014

39

6.36

0.26

2015

40

5.84

0.23

2016

41

6.22

0.27

2017

42

6.33

0.26

2018

43

5.89

0.25

technology activities_22sep/Technology Activity 3 Data sets/Female Breast Cancer.xlsx

Sheet1

Female Breast Cancer

Year

t

New Cases

Death Rate

1975

0

105.08

31.45

1976

1

101.95

31.8

1977

2

100.79

32.48

1978

3

100.59

31.73

1979

4

102.08

31.21

1980

5

102.24

31.68

1981

6

106.36

31.92

1982

7

106.48

32.19

1983

8

111.11

32.07

1984

9

116

32.9

1985

10

124.3

32.98

1986

11

126.86

32.87

1987

12

134.51

32.66

1988

13

131.39

33.2

1989

14

127.29

33.23

1990

15

131.91

33.14

1991

16

133.88

32.69

1992

17

132.13

31.64

1993

18

129.25

31.39

1994

19

131

30.92

1995

20

132.79

30.55

1996

21

133.85

29.49

1997

22

138.12

28.21

1998

23

141.49

27.54

1999

24

141.6

26.61

2000

25

136.68

26.64

2001

26

138.96

26.01

2002

27

135.94

25.62

2003

28

127.13

25.27

2004

29

128.43

24.49

2005

30

126.81

24.14

2006

31

126.5

23.56

2007

32

128.51

22.96

2008

33

128.67

22.55

2009

34

131.1

22.24

2010

35

127.28

21.92

2011

36

130.67

21.55

2012

37

130.44

21.28

2013

38

131.37

20.76

2014

39

131.66

20.58

2015

40

132.02

20.35

2016

41

130.98

20.07

2017

42

132.15

19.89

2018

43

133.01

19.76

technology activities_22sep/Technology Activity 3 Data sets/Liver and Intrahepatic Bile Duct Cancer.xlsx

Sheet1

Liver and Intrahepatic Bile Duct Cancer

Year

t

New Cases

Death Rate

1975

0

2.64

2.81

1976

1

2.66

2.75

1977

2

2.68

2.78

1978

3

2.67

2.74

1979

4

2.68

2.82

1980

5

2.63

2.78

1981

6

2.93

2.87

1982

7

2.94

2.94

1983

8

2.91

2.92

1984

9

2.86

3.02

1985

10

3.16

3.11

1986

11

3.2

3.15

1987

12

3.39

3.2

1988

13

3.39

3.3

1989

14

3.6

3.44

1990

15

3.94

3.61

1991

16

4.33

3.69

1992

17

4

3.91

1993

18

4.51

4.04

1994

19

4.45

4.13

1995

20

4.55

4.36

1996

21

5.42

4.44

1997

22

5.37

4.5

1998

23

5.48

4.59

1999

24

5.84

4.52

2000

25

5.63

4.64

2001

26

5.61

4.72

2002

27

5.76

4.88

2003

28

6.16

5.02

2004

29

6.46

5.13

2005

30

6.86

5.27

2006

31

7.2

5.3

2007

32

7.46

5.37

2008

33

7.66

5.57

2009

34

8.06

5.78

2010

35

8.18

5.91

2011

36

8.6

6.13

2012

37

8.65

6.34

2013

38

8.75

6.48

2014

39

8.88

6.49

2015

40

9.2

6.61

2016

41

9.01

6.67

2017

42

8.89

6.65

2018

43

8.05

6.65

technology activities_22sep/Technology Activity 3 Data sets/Cervical Cancer.xlsx

Sheet1

Cervical Cancer

Year

t

New Cases

Death Rate

1975

0

14.81

5.55

1976

1

14.27

5.43

1977

2

13.02

4.96

1978

3

12.53

4.85

1979

4

12.76

4.58

1980

5

12.25

4.45

1981

6

10.76

4.32

1982

7

10.63

4.1

1983

8

10.5

4.04

1984

9

11.05

3.94

1985

10

10.24

3.82

1986

11

10.79

3.82

1987

12

10.02

3.64

1988

13

10.61

3.61

1989

14

10.7

3.59

1990

15

10.67

3.66

1991

16

10.07

3.49

1992

17

9.94

3.52

1993

18

9.64

3.41

1994

19

9.44

3.38

1995

20

8.91

3.24

1996

21

9.64

3.21

1997

22

9.24

3.14

1998

23

9.13

2.98

1999

24

8.28

2.83

2000

25

7.71

2.78

2001

26

7.96

2.67

2002

27

7.46

2.55

2003

28

7.34

2.49

2004

29

7.18

2.42

2005

30

6.87

2.42

2006

31

6.97

2.42

2007

32

6.67

2.42

2008

33

6.75

2.37

2009

34

6.92

2.29

2010

35

6.8

2.26

2011

36

6.74

2.33

2012

37

6.63

2.29

2013

38

6.41

2.33

2014

39

6.88

2.26

2015

40

6.79

2.27

2016

41

6.49

2.24

2017

42

6.33

2.24

2018

43

6.67

2.17

technology activities_22sep/Technology Activity 3 Data sets/Colorectal Cancer.xlsx

Sheet1

Colorectal Cancer

Year

t

New Cases

Death Rate

1975

0

59.54

28.09

1976

1

61.34

28.58

1977

2

62.39

28.19

1978

3

62.04

28.54

1979

4

62.37

28.15

1980

5

63.75

28.05

1981

6

64.24

27.52

1982

7

62.78

27.24

1983

8

63.66

27.12

1984

9

64.8

27.35

1985

10

66.3

26.93

1986

11

64.18

26.16

1987

12

62.74

25.89

1988

13

61.38

25.28

1989

14

61.7

25.01

1990

15

60.7

24.65

1991

16

59.48

24.01

1992

17

58

23.62

1993

18

56.79

23.31

1994

19

55.64

22.92

1995

20

54.06

22.59

1996

21

54.78

21.86

1997

22

56.41

21.47

1998

23

56.81

21.19

1999

24

55.48

20.93

2000

25

54.15

20.67

2001

26

53.62

20.16

2002

27

53.18

19.76

2003

28

50.84

19.15

2004

29

49.92

18.1

2005

30

47.85

17.56

2006

31

46.9

17.28

2007

32

46.4

16.91

2008

33

45.3

16.46

2009

34

43.31

15.81

2010

35

41

15.51

2011

36

39.68

15.12

2012

37

38.87

14.7

2013

38

37.59

14.49

2014

39

38.66

14.13

2015

40

37.32

14.02

2016

41

38.03

13.7

2017

42

36.6

13.49

2018

43

35.02

13.14

technology activities_22sep/Technology Activity 3 Data sets/Small Intestine Cancer.xlsx

Sheet1

Small Intestine Cancer

Year

t

New Cases

Death Rate

1975

0

1.12

0.34

1976

1

1.01

0.37

1977

2

1.1

0.36

1978

3

1

0.37

1979

4

1.08

0.39

1980

5

1.14

0.36

1981

6

1.04

0.38

1982

7

1.21

0.4

1983

8

1.23

0.4

1984

9

1.21

0.39

1985

10

1.22

0.39

1986

11

1.34

0.4

1987

12

1.49

0.39

1988

13

1.5

0.39

1989

14

1.52

0.39

1990

15

1.3

0.41

1991

16

1.71

0.43

1992

17

1.51

0.4

1993

18

1.67

0.41

1994

19

1.53

0.41

1995

20

1.7

0.42

1996

21

1.69

0.4

1997

22

1.94

0.42

1998

23

1.75

0.39

1999

24

1.93

0.38

2000

25

1.68

0.38

2001

26

1.83

0.38

2002

27

2.08

0.35

2003

28

2.08

0.37

2004

29

1.95

0.37

2005

30

2.18

0.37

2006

31

2.13

0.36

2007

32

2.04

0.34

2008

33

2.2

0.37

2009

34

2.29

0.36

2010

35

2.5

0.36

2011

36

2.38

0.37

2012

37

2.5

0.37

2013

38

2.42

0.36

2014

39

2.39

0.37

2015

40

2.57

0.38

2016

41

2.5

0.42

2017

42

2.53

0.43

2018

43

2.39

0.42

technology activities_22sep/Technology Activity 3 Data sets/Brain and Other Nervous System Cancer.xlsx

Sheet1

Brain and Other Nervous System Cancer

Year

t

New Cases

Death Rate

1975

0

5.85

4.11

1976

1

5.82

4.34

1977

2

6.17

4.4

1978

3

5.76

4.53

1979

4

6.12

4.26

1980

5

6.3

4.37

1981

6

6.51

4.36

1982

7

6.42

4.43

1983

8

6.31

4.39

1984

9

6.12

4.55

1985

10

6.94

4.57

1986

11

6.85

4.53

1987

12

7.01

4.71

1988

13

6.83

4.72

1989

14

6.87

4.73

1990

15

7.05

4.87

1991

16

6.96

4.95

1992

17

6.98

4.85

1993

18

6.76

4.79

1994

19

6.63

4.84

1995

20

6.5

4.67

1996

21

6.69

4.73

1997

22

6.77

4.68

1998

23

6.65

4.68

1999

24

6.93

4.64

2000

25

6.82

4.53

2001

26

6.66

4.45

2002

27

6.79

4.45

2003

28

6.68

4.4

2004

29

6.88

4.31

2005

30

6.78

4.34

2006

31

6.46

4.17

2007

32

6.62

4.21

2008

33

6.75

4.28

2009

34

6.87

4.35

2010

35

6.61

4.25

2011

36

6.71

4.25

2012

37

6.56

4.4

2013

38

6.56

4.34

2014

39

6.36

4.43

2015

40

6.66

4.43

2016

41

6.3

4.49

2017

42

6.32

4.39

2018

43

6.33

4.4

technology activities_22sep/Technology Activity 3 Data sets/Stomach Cancer.xlsx

Sheet1

Stomach Cancer

Year

t

New Cases

Death Rate

1975

0

11.67

8.51

1976

1

12.21

8.3

1977

2

11.54

7.91

1978

3

11.49

7.73

1979

4

12

7.56

1980

5

11.29

7.36

1981

6

11.14

7.25

1982

7

10.92

7.02

1983

8

10.94

6.83

1984

9

10.58

6.78

1985

10

10.22

6.51

1986

11

10.21

6.36

1987

12

10.2

6.18

1988

13

10.2

6.08

1989

14

10.01

6.21

1990

15

9.28

6.07

1991

16

9.71

6

1992

17

9.2

5.63

1993

18

9.03

5.62

1994

19

9.01

5.41

1995

20

8.34

5.35

1996

21

8.48

5.13

1997

22

8.61

4.94

1998

23

8.59

4.81

1999

24

8.58

4.64

2000

25

8.11

4.55

2001

26

7.78

4.37

2002

27

7.98

4.26

2003

28

7.81

4.15

2004

29

7.92

4.01

2005

30

7.48

3.82

2006

31

7.6

3.69

2007

32

7.3

3.64

2008

33

7.26

3.55

2009

34

7.46

3.43

2010

35

7.03

3.42

2011

36

7.26

3.25

2012

37

7.09

3.22

2013

38

6.85

3.18

2014

39

6.69

3.13

2015

40

6.6

3.08

2016

41

6.63

3.02

2017

42

6.63

2.9

2018

43

6.18

2.81

technology activities_22sep/Technology Activity 3 Data sets/Hodgkin Lymphoma.xlsx

Sheet1

Hodgkin Lymphoma

Year

t

New Cases

Death Rate

1975

0

3.09

1.31

1976

1

2.76

1.17

1977

2

2.98

1.14

1978

3

2.8

1.06

1979

4

2.93

0.97

1980

5

2.77

0.98

1981

6

2.92

0.93

1982

7

2.92

0.88

1983

8

3.02

0.85

1984

9

3.06

0.86

1985

10

2.98

0.77

1986

11

2.73

0.78

1987

12

3.04

0.74

1988

13

3.1

0.67

1989

14

3.06

0.71

1990

15

3.06

0.66

1991

16

3.03

0.65

1992

17

2.87

0.65

1993

18

2.86

0.61

1994

19

2.85

0.56

1995

20

2.77

0.55

1996

21

2.86

0.53

1997

22

2.83

0.53

1998

23

2.79

0.48

1999

24

2.85

0.51

2000

25

2.82

0.46

2001

26

2.57

0.47

2002

27

2.96

0.47

2003

28

2.72

0.46

2004

29

2.95

0.43

2005

30

3.03

0.42

2006

31

3.01

0.44

2007

32

3.18

0.41

2008

33

2.96

0.37

2009

34

2.94

0.4

2010

35

2.8

0.38

2011

36

2.73

0.36

2012

37

2.72

0.34

2013

38

2.66

0.32

2014

39

2.81

0.31

2015

40

2.65

0.32

2016

41

2.62

0.27

2017

42

2.3

0.27

2018

43

2.52

0.27

technology activities_22sep/Technology Activity 3 Data sets/Cancer Among Adolescents and Young Adults (AYAs) (Ages 15–39).xlsx

Sheet1

Cancer Among Adolescents and Young Adults (AYAs) (Ages 15–39)

Year

t

New Cases

Death Rate

1975

0

58.13

16.45

1976

1

57.73

16.12

1977

2

59.67

15.88

1978

3

59.01

15.25

1979

4

58.41

15.08

1980

5

58.77

15.33

1981

6

59.91

14.68

1982

7

61.26

14.85

1983

8

62.17

14.49

1984

9

64.55

14.64

1985

10

66.8

14.52

1986

11

68.26

14.42

1987

12

69.75

13.91

1988

13

69.93

13.73

1989

14

71.58

13.55

1990

15

72.91

13.59

1991

16

71.72

13.52

1992

17

72.8

13.38

1993

18

69.23

12.81

1994

19

69.54

12.76

1995

20

69.6

12.53

1996

21

67.64

12.29

1997

22

66.71

12.03

1998

23

65.83

11.8

1999

24

66.68

11.3

2000

25

68.11

11.06

2001

26

68.83

11.11

2002

27

70.54

10.79

2003

28

71.43

10.46

2004

29

72.35

10.06

2005

30

72.98

9.9

2006

31

70.4

9.88

2007

32

74.75

9.49

2008

33

77.36

9.49

2009

34

76.48

9.66

2010

35

74.82

9.33

2011

36

76.07

9.23

2012

37

76.72

9.09

2013

38

75.56

9.02

2014

39

78.91

9.05

2015

40

78.69

8.91

2016

41

80.57

9.04

2017

42

77.1

8.77

2018

43

74.96

8.8

technology activities_22sep/Technology Activity 3 Data sets/Prostate Cancer.xlsx

Sheet1

Prostate Cancer

Year

t

New Cases

Death Rate

1975

0

94

30.97

1976

1

97.95

31.78

1977

2

100.48

31.83

1978

3

99.4

32.66

1979

4

103.42

32.84

1980

5

106.05

33.05

1981

6

108.88

33.17

1982

7

108.25

33.36

1983

8

111.65

33.92

1984

9

111.7

34.06

1985

10

115.52

33.91

1986

11

119.1

34.93

1987

12

133.78

35.11

1988

13

137.65

35.88

1989

14

145.43

37.1

1990

15

171.14

38.56

1991

16

214.89

39.31

1992

17

237.61

39.22

1993

18

209.71

39.34

1994

19

180.43

38.54

1995

20

169.56

37.29

1996

21

169.73

36

1997

22

173.86

34.15

1998

23

171.3

32.63

1999

24

183.73

31.56

2000

25

183.37

30.39

2001

26

185.42

29.52

2002

27

182.76

28.71

2003

28

170.24

27.19

2004

29

166.35

26.19

2005

30

157.18

25.4

2006

31

172.73

24.24

2007

32

175.86

24.23

2008

33

158.79

23.01

2009

34

155.91

22.12

2010

35

148.5

21.81

2011

36

142.47

20.79

2012

37

116.5

19.58

2013

38

111.47

19.29

2014

39

102.23

19.14

2015

40

108.35

18.96

2016

41

110.75

19.39

2017

42

116.67

18.85

2018

43

115.61

18.87

technology activities_22sep/Technology Activity 3 Data sets/Lung and Bronchus Cancer.xlsx

Sheet1

Lung and Bronchus Cancer

Year

t

New Cases

Death Rate

1975

0

52.24

42.56

1976

1

55.41

44.2

1977

2

56.69

45.49

1978

3

57.84

46.88

1979

4

58.62

47.69

1980

5

60.65

49.41

1981

6

62.03

49.99

1982

7

63.29

51.43

1983

8

63.45

52.4

1984

9

65.49

53.36

1985

10

64.62

54.32

1986

11

65.77

55.04

1987

12

67.9

56.24

1988

13

68.06

56.97

1989

14

67.56

57.9

1990

15

68.08

58.85

1991

16

69.19

58.99

1992

17

69.47

58.9

1993

18

67.75

59.13

1994

19

67.16

58.54

1995

20

66.85

58.38

1996

21

66.46

57.91

1997

22

66.63

57.51

1998

23

67.55

57.08

1999

24

65.84

55.42

2000

25

64.14

55.85

2001

26

64.17

55.32

2002

27

64.06

55

2003

28

64.77

54.19

2004

29

62.23

53.37

2005

30

63.04

52.85

2006

31

62.3

51.73

2007

32

62.1

50.71

2008

33

60.39

49.59

2009

34

60.01

48.41

2010

35

57.74

47.42

2011

36

56.26

46.02

2012

37

55.29

44.97

2013

38

54.13

43.48

2014

39

53.28

42.25

2015

40

51.97

40.69

2016

41

51.41

38.52

2017

42

50.05

36.71

2018

43

46.94

34.79

calendar_22sep/calendar_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Course Calendar

The Course Calendar provides an overview of assignment due dates and when to begin each module. For details on each assignment, go to the course website and click the associated module.

Go to

Week-by-Week Dates

to see specific dates for the current semester.

SUMMARY OF ACTIVITIES AND ASSESSMENTS

Activity/Assessment

Week Due

Section in Which to Find Requirements

· Introductions Forum

· Discussion Forum 1

· Practice Exercises 1

1

Module 1

· Technology Activity 1

· Practice Exercises 2

· Module 2 Quiz

2

Module 2

· Technology Activity 2

· Practice Exercises 3

· Module 3 Quiz

3

Module 3

· Discussion Forum 2

· Practice Exercises 4

· Module 4 Quiz

4

Module 4

· Technology Activity 3

· Practice Exercises 5

· Module 5 Quiz

5

Module 5

· Discussion Forum 3

· Practice Exercises 6

6

Module 6

· Practice Midterm Exam

· Midterm Exam

7

Examinations

· Practice Exercises 7

· Module 7 Quiz

8

Module 7

· Technology Activity 4

· Discussion Forum 4

· Practice Exercises 8

· Module 8 Quiz

9

Module 8

· Practice Exercises 9

· Module 9 Quiz

10

Module 9

· Technology Activity 5

· Practice Exercises 10

· Module 10 Quiz

11

Module 10

· Practice Final Exam

· Final Exam

12

Examinations

WEEK-BY-WEEK CALENDAR

Week 1

· Monday—

BEGIN MODULE 1

· Tuesday—Introductions Forum: initial post due

· Wednesday—Discussion Forum 1: initial post due

· Thursday—Introductions Forum: comments due

· Friday—Discussion Forum 1: comments due

· Saturday—

· Sunday—Practice Exercises 1 due

Week 2

· Monday—

BEGIN MODULE 2

· Tuesday—

· Wednesday—

· Thursday—Technology Activity 1 due

· Friday—

· Saturday—Practice Exercises 2 due

· Sunday—Module 2 Quiz due

Week 3

· Monday—

BEGIN MODULE 3

· Tuesday—

· Wednesday—

· Thursday—Technology Activity 2 due

· Friday—

· Saturday—Practice Exercises 3 due

· Sunday—Module 3 Quiz

Week 4

· Monday—

BEGIN MODULE 4

· Tuesday—

· Wednesday—Discussion Forum 2: initial post due

· Thursday—

· Friday—Discussion Forum 2: comments due

· Saturday—Practice Exercises 4 due

· Sunday—Module 4 Quiz

Week 5

· Monday—

BEGIN MODULE 5

· Tuesday—

· Wednesday—

· Thursday—Technology Activity 3 due

· Friday—

· Saturday—Practice Exercises 5 due

· Sunday—Module 5 Quiz

Week 6

· Monday—

BEGIN MODULE 6

· Tuesday—

· Wednesday—Discussion Forum 3: initial post due

· Thursday—

· Friday—Discussion Forum 3: comments due

· Saturday—Practice Exercises 6 due

· Sunday—

Week 7

Midterm Exam Week: Take exam by Sunday of Week 7.

· Monday—

· Tuesday—

· Wednesday—Practice Midterm Exam due

· Thursday—

· Friday—

· Saturday—

· Sunday—Midterm Exam due

Week 8

· Monday—

BEGIN MODULE 7

· Tuesday—

· Wednesday—

· Thursday—

· Friday—

· Saturday—Practice Exercises 7 due

· Sunday—Module 7 Quiz

Week 9

· Monday—

BEGIN MODULE 8

· Tuesday—

· Wednesday—Technology Activity 4 due

· Thursday—Discussion Forum 4: initial post due

· Friday—

· Saturday—Discussion Forum 4: comments due; Practice Exercises 8 due

· Sunday—Module 8 Quiz

Week 10

· Monday—

BEGIN MODULE 9

· Tuesday—

· Wednesday—

· Thursday—

· Friday—

· Saturday—Practice Exercises 9 due

· Sunday—Module 9 Quiz

Week 11

· Monday—

BEGIN MODULE 10

· Tuesday—

· Wednesday—

· Thursday—Technology Activity 5 due

· Friday—

· Saturday—Practice Exercises 10 due

· Sunday—Module 10 Quiz due

Week 12

Final Exam Week: Take exam by Sunday of Week 12.

· Monday—

· Tuesday—

· Wednesday—Practice Final Exam due

· Thursday—

· Friday—

· Saturday—

· Sunday—Final Exam due

Copyright © 2022 by Thomas Edison State University. All rights reserved.

exam study guides_22sep/final exam study guide_MAT-121-sep22 x

MAT-121 • College Algebra

Final Exam Study Guide

©2022 Thomas Edison State University

All Rights Reserved

Exam Details

Modules assessed: 7–10

Materials allowed: graphing calculator

Duration: 3 hours

Exam Format

Multiple choice: 25 questions • apply concepts to solve problems

Correct answers are worth 4 points. Some “nearly correct” answers are worth 2 points.

Tips from the Test Development Team

·

How to Use the Study Guide to Help Prepare for Your Exam

·

How to Answer Multiple-Choice Questions

*Note: Use this study guide to prepare for your Practice Final Exam, which is a required activity, as well as your Final Exam. The questions on the practice exam closely resemble those on the actual exam. Also review the video solutions to selected quiz questions, which also closely resemble exam questions.

Module 7

· Rewriting Quadratics in Standard Form

· Polynomial Functions and Real-World Applications

· Writing Formulas for Polynomial Functions

· Graphing Polynomial Functions

· Identifying Zeros and Their Multiplicities

Module 8

· Synthetic Division

· Polynomial Division

· Remainder Theorem

· Factor Theorem

· Asymptotes and Intercepts of Rational Functions

· Writing Rational Functions

Module 9

· Compound Interest Formula

· Graphing Transformations of Exponential Functions

· Using Common Logarithms and Real-World Applications

· Converting from Exponential to Logarithmic Form

· Graphing Logarithmic Functions and Transformations

Module 10

· Logarithmic Properties

· Change-of-Base Formula

· Solving Logarithmic Equations

· Modeling Exponential Growth and Decay

· Using Newton’s Law of Cooling

· Using Logistic Growth Models

· Graphing Logarithmic Functions; Finding the Domain of a Logarithmic Function; Example 10 (Finding the Vertical Asymptote of a Logarithm Graph)

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MAT-121 • College Algebra

Midterm Exam Study Guide

©2022 Thomas Edison State University

All Rights Reserved

Exam Details

Modules assessed: 2–5

Materials allowed: graphing calculator

Duration: 3 hours

Exam Format

Multiple choice: 25 questions • apply concepts to solve problems

Correct answers are worth 4 points. Some “nearly correct” answers are worth 2 points.

Tips from the Test Development Team

·

How to Use the Study Guide to Help Prepare for Your Exam

·

How to Answer Multiple-Choice Questions

*Note: Use this study guide to prepare for your Practice Midterm Exam, which is a required activity, as well as your Midterm Exam. The questions on the practice exam closely resemble those on the actual exam. Also review the video solutions to selected quiz questions, which also closely resemble exam questions.

Module 2

· Finding a Linear Equation and Real-World Applications

· Using the Distance Formula and Real-World Applications

· Determining Whether Lines Are Parallel or Perpendicular

· Finding a Linear Equation and Models and Applications

· Using the Distance Formula and Models and Applications

Module 3

· Simplifying Powers of

i and Evaluating Complex Equations

· Solving Quadratic Equations by Factoring

· Solving Quadratic Equations by Using the Quadratic Formula

· Solving Inequalities

· Solving Absolute Value Inequalities

Module 4

· Finding Input and Output Values of a Function

· Function Notation

· Finding Domain and Range from Graphs and Using Notations to Specify Domain and Range

· Piecewise Defined Functions (Example 12, Working with a Piecewise Function)

· Average Rate of Change

· Local/Absolute, Minima/Maxima

· Composition of Functions and Real-World Application

Module 5

· Toolkit Functions and Transformations of Functions

· Function Transformations and Using Vertical and Horizontal Shifts

· Finding the Slope of a Line

· Parallel/Perpendicular Lines

· Linear Functions and Modeling with Linear Functions

· Linear Regression

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MAT-121: COLLEGE ALGEBRA

Module 1—Review of Pre-Algebraic Concepts, Part 1

OVERVIEW

Welcome to College Algebra! This course will provide you with critical skills that have practical applications in business, science, healthcare, teaching, design, or any job that requires some degree of analytical thinking. College Algebra builds the necessary foundation for higher level mathematics such as precalculus and calculus. We will use technology like Geogebra and Desmos to enhance the understanding of the algebraic concepts covered throughout the course.

Module 1 consists of an introduction to successful study skills and a review of pre-algebraic concepts. Pre-algebra refers to the prerequisite arithmetic and geometry knowledge needed for algebra. Module 1 is part 1 of the review of pre-algebraic concepts; Module 6 is part 2. We will create a basic algebraic foundation that will be used for problem-solving throughout the course.

TOPICS

Module 1 covers the following topics:

· Study skills

· Real numbers

· Order of operations

· Algebraic expressions

· Exponents

· Scientific notation

· Radicals

· Rational exponents

OBJECTIVES

After successfully completing Module 1, you should be able to:

MO 1.1 Create a plan for improving mathematical study skills. [CO 1, CO 2]

MO 1.2 Classify a real number as natural, whole, integer, rational, or irrational. [CO 1, CO 2]

MO 1.3 Perform calculations on real numbers using order of operations and properties of real numbers. [CO 1, CO 2]

MO 1.4 Use the properties of exponents to simplify algebraic expressions. [CO 1, CO 2]

MO 1.5 Apply scientific notation to real-world applications. [CO 1, CO 2]

MO 1.6 Use the properties of radicals to simplify radical expressions. [CO 1, CO 2]

MO 1.7 Use the properties of rational exponents to simplify expressions. [CO 1, CO 2]

STUDY MATERIALS

Textbook Readings

· Chapter 1, sections 1.1 through 1.3 in Abramson,

College Algebra

Required Materials

·

Study Skills Survey

·

Plan for Improvement

Additional Materials

· CK-12. (2022, January 17).

Scientific notation

. CK-Foundation.

· CK-12. (n.d.).

Properties of exponents

. CK-Foundation.

· CK-12. (n.d.).

The real numbers: Number system

. CK-12 PLIX Series.

· CK-12. (n.d.).

Negative and zero exponents: Patterns with powers

. CK-12 PLIX Series.

· CK-12. (n.d.).

Multiplication and division of radicals: Totally radical dude’s height

. CK-12 PLIX Series.

· Bolte, J. (2011, March 7).

Scientific notation

. Wolfram Demonstrations Project.

· Nevell, J. (2011, November 16).

Integer exponents

. Wolfram Demonstrations Project.

· Beck, G. (2011, March 7).

Laws of exponents

. Wolfram Demonstrations Project.

· Khan Academy. (n.d.).

Radicals and rational exponents

.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 1.1: exercises 5, 7, 31, 39, 49, 53

·

Section 1.2: exercises 27, 39, 47, 49

·

Section 1.3: exercises 27, 31, 41, 57, 66

ACTIVITIES

Module 1 has three activities. Please consult the Course Calendar for the due dates.

Introductions Forum (Video Post)

As we start this course, let’s get to know each other a bit. Learning about each other will help us have more productive and engaging discussions throughout the semester.

Introduce yourself to your classmates and mentor in a video, and let us know the following:

· Your reasons for taking this course

· Your work experience and/or future career goals

· The last math class you took (state course name and year taken)

· How you’re feeling about taking this course (curious, confident, anxious, etc.)

Then, find an appropriate photograph or object that tells us something significant about yourself. Tell us about it and share why it’s important to you.

Reply with a written response to

at least two classmates’ video posts by the date indicated in the Course Calendar. In your replies, tell them if you have anything in common with them, or ask them questions about something they’ve shared that interests you. If you have insights or advice about something they’ve said, let them know.

Note: The Introductions Forum is not graded but is required.

For instructions on how to record and upload your video response, review the following document:

Using Video Tools in Moodle

.

Discussion Forum 1

at least two classmates’ responses by the date indicated in the Course Calendar.

Reflect on your past math experiences and create a plan for improvement. Download and fill out the two documents linked in the Required Materials section: Study Skills Survey and Plan for Improvement. Submit both completed documents to your mentor. Then, create a discussion forum thread where you share your completed Plan for Improvement document and also address the following questions:

· What was your score from the completed Study Skills Survey?

· Did your score surprise you? Why or why not?

· What challenges do you face, and what are some possible solutions?

Reply to

at least two posts by other students. In your replies, note whether you have any similar challenges as your classmates. Are there any challenges or possible solutions your classmates have that may assist your improvement plan? [MO 1.1]

Practice Exercises 1

In each module of this course, you will complete practice exercises to help reinforce the skills you are learning. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 1.2 through MO 1.7]

Assignment sheet for Practice Exercises 1

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 10—Exponential and Logarithmic Functions, Part 2

OVERVIEW

Welcome to the final module! It’s time to explore logarithmic properties and their close relationship to exponential properties. You’ll utilize these properties to solve real-world exponential and logarithmic models like Newton’s law of cooling, exponential growth of viruses, and the logistic growth model. For the last technology activity, you will use Desmos and exponential regression to fit a model to real-world radioactive isotope data.

TOPICS

Module 10 covers the following topics:

· Logarithmic properties

· Change-of-base formula

· Exponential and logarithmic equations

· Exponential and logarithmic models

· Newton’s law of cooling

· Logistic-growth model

· Fitting exponential models to data

OBJECTIVES

After successfully completing Module 10, you should be able to:

MO 10.1 Apply logarithmic properties. [CO 1, CO 2, CO 4]

MO 10.2 Solve exponential and logarithmic equations. [CO 1, CO 2, CO 4, CO 5, CO 6]

MO 10.3 Solve applied problems using exponential and logarithmic equations. [CO 1, CO 2, CO 4, CO 5, CO 6]

MO 10.4 Model exponential growth and decay. [CO 1, CO 2, CO 4, CO 5]

MO 10.5 Use Newton’s law of cooling to solve real-world problems. [CO 1, CO 2, CO 6]

MO 10.6 Model exponential data using regression. [CO 1, CO 2, CO 5 CO 7]

MO 10.7 Use the logistic growth model to solve problems. [CO 1, CO 2, CO 5, CO 7]

MO 10.8 Apply change-of-base formula. [CO 1, CO 2, CO 5, CO 7]

MO 10.9 Find the domain, vertical asymptotes, and end behavior for logarithmic functions. [CO 1, CO 2, CO 5, CO 7]

STUDY MATERIALS

Textbook Readings

· Chapter 6, sections 6.5 through 6.8 in Abramson,

College Algebra

Additional Materials

· Khan Academy. (n.d.).

Solve exponential equations using exponent properties

.

· Khan Academy. (n.d.).

Interpret change in exponential models

.

· Khan Academy. (n.d.).

Construct exponential models

.

· Khan Academy. (n.d.).

Intro to logarithm properties

.

· Khan Academy. (n.d.).

Justifying the logarithm properties

.

· Khan Academy. (n.d.).

Logarithm change of base rule intro

.

· Khan Academy. (n.d.).

What are the logarithm properties?

· Khan Academy. (n.d.).

Solving exponential equations using logarithms

.

· Khan Academy. (n.d.).

Exponential model word problems

.

· CK-12. (n.d.).

Logarithm properties: The log properties

. CK-12 PLIX Series.

· Rivas, A. (2011, March 7).

Calculating integer logarithms in different bases

. Wolfram Demonstrations Project.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 6.5: exercises 11, 19, 23, 31, 33

·

Section 6.6: exercises 5, 26, 35, 37, 47, 55, 71, 77

·

Section 6.7: exercises 7, 15, 21, 33, 43, 52

·

Section 6.8: exercises 31, 32, 33, 41, 42, 43

ACTIVITIES

Module 10 has three activities. Please consult the Course Calendar for the due dates.

Technology Activity 5

In your last technology activity of the course, you will use Desmos and exponential regression to model real-world radioactive isotope data. A tool in Desmos, called a

slider, will be used to manipulate the decay rate to model your equation as close as possible to your data. [MO 10.6]

Technology Activity 5

Submit Technology Activity 5 and all your graph exports to your mentor for grading.

Practice Exercises 10

You have made it to the last set of practice exercises! As you have been doing all along, you’ll reinforce this module’s skills by completing practice exercises that are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 10.1 through MO 10.9]

Assignment sheet for Practice Exercises 10

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 10 Quiz

The Module 10 quiz is the last quiz in this course! Like all of the previous quizzes, it is multiple choice, open book, untimed, and unproctored. A graphing calculator is provided as a tool within the quiz. Practice using this calculator, which is also provided on your exams.

Each module quiz includes some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

Remember to think of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. [MO 10.1, MO 10.2, MO 10.3, MO 10.4, MO 10.5, MO 10.6]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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modules_22sep/module 2_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Module 2—Equations and Inequalities, Part 1

OVERVIEW

Welcome to Module 2! Now that we have reviewed pre-algebraic concepts, we are ready to build our foundation for solving and graphing equations. In this module you will learn about the Cartesian coordinate system (CCS) and graphing. The CCS has important practical applications including GPS systems, satellite technology, maps, and city planning and designing.

A highlight of this module is your first technology activity, in which you’ll investigate parallel and perpendicular lines using Geogebra, a free interactive math tool. The required practice exercises and formative quiz will also help you reinforce your knowledge and prepare for upcoming modules.

TOPICS

Module 2 covers the following topics:

· Cartesian coordinate system

· Intercepts

· Linear equations in one variable

· Rational equations

· Parallel and perpendicular lines

· Models and applications

OBJECTIVES

After successfully completing Module 2, you should be able to:

MO 2.1 Plot ordered pairs in a Cartesian coordinate system. [CO 1, CO 3]

MO 2.2 Graph equations by plotting points and finding the x and y intercepts. [CO 1, CO 3]

MO 2.3 Use the midpoint and distance formulas, given two points, and apply them to real-world applications. [CO 1, CO 2, CO 6]

MO 2.4 Solve various forms of linear equations in one variable. [CO 1, CO 2, CO 4]

MO 2.5 Determine if the graphs of the equations of two lines are perpendicular, parallel, or neither. [CO 1, CO 2, CO 4]

MO 2.6 Write the equation of a line parallel or perpendicular to a given line. [CO 1, CO 2, CO 4]

MO 2.7 Model and solve linear equations involving real-world applications. [CO 1, CO 2, CO 6]

STUDY MATERIALS

Textbook Readings

· Chapter 2, sections 2.1 through 2.3 in Abramson,

College Algebra

Additional Materials

· Khan Academy. (n.d.).

Intercepts of lines review (x-intercepts and y-intercepts)

.

· Hafner, I. (2014, May 1).

Solving a linear equation in one variable and two parameters

. Wolfram Demonstrations Project.

· CK-12. (n.d.).

Points in the coordinate plane

. CK-12 PLIX Series.

· CK-12. (n.d.).

Graphs of linear equations: Let’s play mini-golf

. CK-12 PLIX Series.

· CK-12. (n.d.).

Slope-intercept form of linear equations: Mountain train

. CK-12 PLIX Series.

·

Desmos. Lines: Slope Intercept Form

·

V

ideo Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 2.1: exercises 5, 11, 17, 23, 31, 35, 39, 49

·

Section 2.2: exercises 11, 21, 27, 33, 37, 41, 45

·

Section 2.3: exercises 7, 9, 17, 25, 47

ACTIVITIES

Module 2 has three activities. Please consult the Course Calendar for the due dates.

Technology Activity 1

During this course, you will complete several technology activities that are designed to require practical, hands-on application of the algebraic skills you are learning. You will develop technical skills to solve real-world problems and answer complex questions.

In this first technology activity, you will investigate parallel and perpendicular lines using technology. Parallel and perpendicular lines are very important mathematical concepts used in the designing and building of roads, home and building construction, map making, electrical circuit design and layout, clothing and textile manufacturing, and sports (just to name a few.) Using Geogebra, you will use the available features to create lines, determine the equations of each line, find slope, and create lines parallel to your created lines. Likewise, you will do a similar investigation using the perpendicular line feature in Geogebra. [MO 2.1, MO 2.2, MO 2.5, MO 2.6]

Technology Activity 1

Submit Technology Activity 1 and all your graph exports to your mentor for grading.

Practice Exercises 2

As you did in the last module, you will again complete practice exercises to help reinforce the skills you are learning. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 2.1 through MO 2.7]

Assignment sheet for Practice Exercises 2

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 2 Quiz

Most modules in this course include a quiz. Think of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. You will be in excellent shape for your exams if you take your time on quizzes, pay close attention to the feedback you receive at the end, and use these tools to develop your skills.

In this module you will take your first quiz. Like every quiz in this course, it consists of multiple-choice problems focusing on what you’re learning in the module. The quiz is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams.

Each module quiz includes some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook. [MO 2.1 through MO 2.7]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 3—Equations and Inequalities, Part 2

OVERVIEW

Welcome to Module 3! This module is an introduction to complex numbers, which consist of real and imaginary numbers. Complex numbers have applications in advanced mathematics, physics, and engineering. This module also includes an introduction to quadratic equations and methods of solving quadratic equations. The graphs of quadratic equations can be seen all around us, such as the Gateway Arch in St. Louis and the symbol for McDonald’s. Inequalities are introduced with interval and set builder notation to represent their solution along with displaying solutions on a number line. The second technology activity covers an investigation into quadratic equations and inequalities using Geogebra and Desmos.

TOPICS

Module 3 covers the following topics:

· Complex numbers

· Quadratic equations

· Factoring

· Square root property

· Completing the square

· Quadratic formula and the discriminant

· Inequalities

OBJECTIVES

After successfully completing Module 3, you should be able to:

MO 3.1 Plot complex numbers in a Cartesian coordinate system. [CO 1, CO 3]

MO 3.2 Perform arithmetic operations on complex numbers and simplify powers of

i. [CO 1, CO 2, CO 4]

MO 3.3 Solve quadratic equations using various methods. [CO 1, CO 2, CO 4]

MO 3.4 Solve linear and absolute value inequalities using properties of inequalities and technology. [CO 1, CO 2, CO 8]

STUDY MATERIALS

Textbook Readings

· Chapter 2, sections 2.4, 2.5, and 2.7 in Abramson,

College Algebra

Additional Materials

· Khan Academy. (n.d.).

Intro to complex numbers

.

· Khan Academy. (n.d.).

Solving absolute value inequalities 1

[Video].

· Khan Academy. (n.d.).

Solving absolute value inequalities 2

[Video].

· Rivas, A. (2011, March 7).

Solution of quadratic equations

. Wolfram Demonstrations Project.

· Hafner, I. (2014, April 16).

Solving linear inequalities

. Wolfram Demonstrations Project.

· CK-12. (n.d.).

Inequality expressions: Inequality graph

. CK-12 PLIX Series.

· CK-12. (n.d.).

Multi-step inequalities: Summer camp

. CK-12 PLIX Series.

· Veera, C. (n.d.).

Graphing compound inequalities

on number

line

. GeoGebra.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 2.4: exercises 7, 11, 17, 33, 43, 55

·

Section 2.5: exercises 7, 23, 29, 37, 47, 53

·

Section 2.7: exercises 7, 13, 17, 23, 25, 29, 35, 45, 47, 51

ACTIVITIES

Module 3 has three activities. Please consult the Course Calendar for the due dates.

Technology Activity 2

As you know, this course requires several technology activities that are designed to provide practical, hands-on application of the algebraic skills you are learning. You will develop technical skills to solve real-world problems and answer complex questions.

For Technology Activity 2, you will use technology (a graphing calculator or online graphing utility like Desmos and Geogebra) to investigate quadratic equations and linear and absolute value inequalities. The graphs of quadratics are called parabolas and are used in the designs of parabolic objects like radio telescopes and satellite dishes. Inequalities are used in the manufacturing process of materials that must meet a certain tolerance in their specifications. This activity will help prepare you for professional tasks requiring knowledge of algebra. [MO 3.1 through MO 3.4]

Technology Activity 2

Submit Technology Activity 2 and all your graph exports to your mentor for grading.

Practice Exercises 3

By now you are getting accustomed to practice exercises. This module’s exercises, like those in every module, will help reinforce the skills you are learning. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 3.1 through MO 3.4]

Assignment sheet for Practice Exercises 3

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 3 Quiz

The Module 3 quiz consists of multiple-choice problems focusing on what you’re learning in this module. The quiz is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams.

Remember to think of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. [MO 3.3, MO 3.4]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 4—Functions

OVERVIEW

Welcome to Module 4! This module is an introduction to one of the most powerful concepts in mathematics, the function. Functions are used extensively in higher mathematics (calculus), physics, and engineering. They are also used in real-world technologies including vending machines, ATMs, self-serve car washes, change machines in laundromats, and automatic IV machines (a liquid/medicine is dripped into a patient’s vein at a constant rate). You will learn the characteristics of a function, as well as graphing and modeling linear functions including real-world applications.

TOPICS

Module 4 covers the following topics:

· Functions and function notation

· Vertical line test

· Domain and range

· Rates of change

· Behavior of graphs

· Composite functions

· Transformations

OBJECTIVES

After successfully completing Module 4, you should be able to:

MO 4.1 Determine if a relation represents a function utilizing various techniques (definition and the vertical line test). [CO 1, CO 2, CO 3]

MO 4.2 Determine if a function is one-to-one. [CO 1, CO 2, CO 3]

MO 4.3 Evaluate functions for given values of a variable. [CO 1, CO 2, CO 4]

MO 4.4 Write relations and equations in function notation. [CO 1, CO 2, CO 4]

MO 4.5 Graph a variety of functions. [CO 1, CO 2, CO 3]

MO 4.6 Find the range and domain of a function. [CO 1, CO 2]

MO 4.7 Find the average rate of change (slope) of a function. [CO 1, CO 2]

MO 4.8 Use a graph to determine if the function is increasing or decreasing and locate any extrema. [CO 1, CO 2, CO 3]

MO 4.9 Determine the composition of two or more functions and find its domain. [CO 1, CO 2, CO 4]

STUDY MATERIALS

Textbook Readings

· Chapter 3, sections 3.1 through 3.4 in Abramson,

College Algebra

Additional Materials

· CK-12. (2016, February 18).

Functions

. CK-12 Foundation.

· CK-12. (n.d.).

Identify functions and the vertical line test: Vertical line test

. CK-12 PLIX Series.

· CK-12. (n.d.).

Composition of functions: Composite functions

. CK-12 PLIX Series.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 3.1: exercises 9, 29, 41, 53, 57, 61, 63, 71, 81, 89

·

Section 3.2: exercises 9, 29, 41, 49, 53

·

Section 3.3: exercises 7, 17, 19, 27, 31, 39, 45

·

Section 3.4: exercises 5, 13, 19, 27, 43, 57, 67, 73, 91

ACTIVITIES

Module 4 has three activities. Please consult the Course Calendar for the due dates.

Discussion Forum 2

In Discussion Forum 2, post your response to the following discussion question. Reply to

at least two classmates’ responses by the date indicated in the Course Calendar.

Using either a stairway or a handicap access ramp (specific data values given), model a linear function and determine if the stairs/ramp are “up to code” based on International Building Codes (stairs) or ADA ramp requirements. [MO 4.3, MO 4.4, MO 4.6]

Option 1—Stairs

Measure the rise and run of several steps and calculate the equation of the line of the stairs.

Option 2—Ramp

Choose one from each set and post the values to the forum. You must choose a pair of values not already selected by a classmate.

Height list: 24.5, 25, 25.5, 26, 26.5, 27, 27.5, 28, 28.5, 29, 29.5

Slope ratio: 1:12, 1:12.5, 1:13, 1:13.5, 1:14, 1:14.5, 1:15

Practice Exercises 4

You are nearing the halfway point of this course. To help reinforce the skills you are learning in Module 4, you will complete practice exercises based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 4.1 through MO 4.9]

Assignment sheet for Practice Exercises 4

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 4 Quiz

By now you are getting used to taking module quizzes. Keep in mind that these are meant to be skill-building activities. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

Each module quiz, including this one, has some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due.

Looking ahead, now is also a good time to start reading the Midterm Exam Study Guide located in the Assessments section of your course space. It lists all of the topics and skills you’ll need for the exam. If anything on it is unfamiliar as you prepare for the exam, be sure to review your textbook, re-watch the quiz solution videos, or speak with your mentor.

Like every quiz in this course, this one consists of multiple-choice problems focusing on what you’re learning in the module. The quiz is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams. [MO 4.3, MO 4.4, MO 4.5, MO 4.6, MO 4.7]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 5—Linear Functions

OVERVIEW

Welcome to Module 5! We will be halfway through the course after completion of this module. This module looks specifically at linear functions. You will expand the concept of a function to linear equations. Linear functions will be graphed and modeled including real-world applications. The third technology activity is an introduction to linear function regression using real-world data collected by the SEER Program (cancer related data). The linear function created from this regression analysis can be used for modeling future trends in predicting cancer and helping with cancer research.

TOPICS

Module 5 covers the following topics:

· Linear functions

· Modeling with linear functions

· Fitting linear models to data

OBJECTIVES

After successfully completing Module 5, you should be able to:

MO 5.1 Identify and graph function transformation. [CO 1, CO 2, CO 3, CO 4]

MO 5.2 Determine if a function is odd, even, or neither. [CO 1, CO 2]

MO 5.3 Translate linear equations into linear functions. [CO 1, CO 2]

MO 5.4 Interpret slope as a rate of change. [CO 1, CO 2]

MO 5.5 Graph linear functions. [CO 1, CO 2, CO 3]

MO 5.6 Determine if two lines are parallel or perpendicular. [CO 1, CO 2]

MO 5.7 Write equations of parallel and perpendicular lines. [CO 1, CO 2, CO 4]

MO 5.8 Model linear functions from real-world applications. [CO 1, CO 2, CO 5, CO 6]

MO 5.9 Graph and interpret scatter plots; use a graphing utility to find the best line of fit

from real-world data. [CO 1, CO 2, CO 3, CO 6, CO 7]

STUDY MATERIALS

Textbook Readings

· Chapter 3, section 3.5 and Chapter 4, sections 4.1 through 4.3 in Abramson,

College Algebra

Additional Materials

· Hafner, I. (2011, March 7).

Linear function game

. Wolfram Demonstrations Project.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 3.5: exercises 9, 19, 25, 29, 35, 43, 49, 59, 67, 75

·

Section 4.1: exercises 11, 17, 25, 29, 39, 45, 49, 55, 61, 73, 87

·

Section 4.2: exercises 9, 25, 49, 55

·

Section 4.3: exercises 9, 19, 23, 39

ACTIVITIES

Module 5 has three activities. Please consult the Course Calendar for the due dates.

Technology Activity 3

Technology Activity 3 will expand your practical experience using the skills you are developing in this course.

In this activity, you will use real-world cancer research data from the SEER (Surveillance, Epidemiology, and End Results) program and technology for linear regression to find the best line of fit. The line found can be used to predict future trends in the specific cancer data you chose relating to the number of new cases and death rate (Geogebra graphing utility). [MO 5.4, MO 5.9]

Technology Activity 3

Submit Technology Activity 3 and all your graph exports to your mentor for grading.

Practice Exercises 5

You will complete practice exercises to help reinforce the skills you are learning in Module 5. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 5.1 through MO 5.9]

Assignment sheet for Practice Exercises 5

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 5 Quiz

The Module 5 quiz consists of multiple-choice problems focusing on what you’re learning in this module. The quiz is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams.

Keep in mind that each module quiz includes some problems that closely resemble those that will appear on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

As always, think of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. [MO 5.1, MO 5.3, MO 5.4, MO 5.6, MO 5.7, MO 5.8]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 6—Review of Pre-Algebraic Concepts, Part 2

OVERVIEW

Welcome to Module 6! In this module you will continue your review of pre-algebraic concepts that began in Module 1. The module covers polynomials, factoring polynomials, and rational expressions and is the foundation for Module 7 on polynomial and rational functions. You will also take a survey of exam study skills and create a plan for success when taking mathematics exams. The survey and plan can then be utilized throughout your educational career.

TOPICS

Module 6 covers the following topics:

· Polynomials

· Factoring polynomials

· Rational expressions

OBJECTIVES

After successfully completing Module 6, you should be able to:

MO 6.1 Formulate a plan for mathematics exam success. [CO 1]

MO 6.2 Classify and identify the degree of polynomials. [CO 1, CO 2, CO 4]

MO 6.3 Perform basic operations on polynomials. [CO 1, CO 2, CO 4]

MO 6.4 Factor polynomials using various techniques. [CO 1, CO 2, CO 4]

MO 6.5 Perform basic operations to simplify rational expressions. [CO 1, CO 2, CO 4]

MO 6.6 Simplify complex rational expressions. [CO 1, CO 2, CO 4]

STUDY MATERIALS

Textbook Readings

· Chapter 1, sections 1.4 through 1.6 in Abramson,

College Algebra

Required Materials

·

P

lan for Success

·

Mathematics Exam Study Skills Survey

Additional Materials

· Khan Academy. (n.d.).

Adding and subtracting polynomials review

.

· Khan Academy. (n.d.).

Multiplying monomials by polynomials review

.

· Khan Academy. (n.d.).

Multiplying binomials by polynomials review

.

· Khan Academy. (n.d.).

Intro to rational expressions

.

· CK-12. (n.d.).

Polynomials in standard form

. CK-12 PLIX Series.

· CK-12. (n.d.).

Addition and subtraction of polynomials: Splitting into tiles

. CK-12 PLIX Series.

· CK-12. (n.d.).

Multiply polynomials by binomials: Rainbows

. CK-12 PLIX Series.

· CK-12. (n.d.).

Special products of polynomials: Difference of two squares

. CK-12 PLIX Series.

· CK-12. (n.d.).

Factor quadratics: Algebra tiles

. CK-12 PLIX Series.

· CK-12. (n.d.).

Factor by grouping: Polynomials

. CK-12 PLIX Series.

· CK-12. (n.d.).

Multiplication of rational expressions

. CK-12 PLIX Series.

· CK-12. (n.d.).

Division of rational expressions: Step by step

. CK-12 PLIX Series.

· Nochella, J. (2011, March 7).

Squaring a binomial

. Wolfram Demonstrations Project.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 1.4: exercises 17, 27, 35, 43, 47, 51

·

Section 1.5: exercises 15, 23, 27, 35, 53, 61, 67

·

Section 1.6: exercises 15, 47, 49, 63, 71, 79

ACTIVITIES

Module 6 has two activities. Please consult the Course Calendar for the due dates.

Discussion Forum 3

at least two classmates’ responses by the date indicated in the Course Calendar.

Reflect on your past experiences in taking math exams and create a plan for success using a growth mindset. Download and fill out the two documents linked in the Required Materials section: Mathematics Exam Study Skills Survey and Plan for Success. Submit both completed documents to your mentor. Then, create a discussion forum thread where you share your completed Plan for Success document and address the following questions:

· What was your score from the completed Mathematics Exam Study Skills Survey?

· Did your score surprise you? Why or why not?

· What challenges do you face, and what are some possible solutions?

Reply to

at least two posts by other students. In your replies, note whether you have any similar challenges as your classmates. Are there any challenges or possible solutions your classmates have that may assist your improvement plan? [MO 6.1]

Practice Exercises 6

As you have been doing in each module, you will complete practice exercises to help reinforce the skills you are learning. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 6.1 through MO 6.6]

Assignment sheet for Practice Exercises 6

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 7—Polynomial and Rational Functions, Part 1

OVERVIEW

Welcome to Module 7! This module expands upon the content covered in Module 6 by looking at all aspects of polynomial functions including quadratic and power functions: increasing/decreasing, extrema, zeros, and graphing. Polynomial functions have real-world applications in the volume of boxes, cylinders, and other forms of product containers.

TOPICS

Module 7 covers the following topics:

· Quadratic functions

· Power functions and polynomial functions

· Graphs of polynomial functions

OBJECTIVES

After successfully completing Module 7, you should be able to:

MO 7.1 Write quadratic equations in various forms (vertex, general, and standard). [CO 1, CO 2, CO 4]

MO 7.2 Solve real-world applications using the quadratic/polynomial function model. [CO 1, CO 2, CO 5]

MO 7.3 Identify power functions and their end behavior. [CO 1, CO 2, CO 4]

MO 7.4 Find the degree and leading coefficient of polynomial functions. [CO 1, CO 2, CO 4]

MO 7.5 Graph polynomial functions and identify all the significant features. [CO 1, CO 2, CO 3, CO 4]

MO 7.6 Write polynomial functions given a graph or information about a polynomial graph. [CO 1, CO 2, CO 4]

MO 7.7 Find the zeros and multiplicity of polynomial functions. [CO 1, CO 2, CO 4]

MO 7.8 Determine the minimum/maximum, domain/range, and axis of symmetry of polynomial functions. [CO 1, CO 2, CO 4]

STUDY MATERIALS

Textbook Readings

· Chapter 5, sections 5.1 through 5.3 in Abramson,

College Algebra

Additional Materials

· Khan Academy. (n.d.).

Solving quadratics by taking square roots

.

· Khan Academy. (n.d.).

Solving simple quadratics review

.

· Khan Academy. (n.d.).

Graph quadratics in vertex form

.

· Khan Academy. (n.d.).

Quadratic word problems (vertex form)

.

· CK-12. (n.d.).

Graph quadratic functions and equations: Soccer ball trajectory

. CK-12 PLIX Series.

· Pegg Jr., E. (2011, March 7).

End behavior of polynomial functions

. Wolfram Demonstrations Project.

· Zaborowski, E. (2011, March 7).

Polynomial graph generator

. Wolfram Demonstrations Project.

· Weisstein, E. (2007, April 27).

Cubic polynomial

. Wolfram Demonstrations Project.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 5.1: exercises 17, 27, 35, 43, 47, 51

·

Section 5.2: exercises 15, 23, 27, 35, 53, 61, 67

·

Section 5.3: exercises 15, 47, 49, 63, 71, 79

ACTIVITIES

Module 7 has two activities. Please consult the Course Calendar for the due dates.

Practice Exercises 7

As you start approaching the last modules of this course, you will continue to reinforce your skills by completing practice exercises. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 7.1 through MO 7.8]

Assignment sheet for Practice Exercises 7

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 7 Quiz

Now that you are in the second half of the course, you know what to expect from module quizzes. The Module 7 quiz consists of multiple-choice problems focusing on what you’re learning in this module. The quiz is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams.

Keep in mind that each module quiz includes some problems that closely resemble problems that you’ll see on your exams. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

Keep thinking of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. [MO 7.1 through MO 7.6]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 8—Polynomial and Rational Functions, Part 2

OVERVIEW

Welcome to Module 8! This module expands upon the previous module on polynomial functions by finding the zeros of polynomials, applying long and synthetic division on polynomials, and applying the following theorems: rational root theorem, intermediate value theorem, Descartes’ rule of signs, and investigating end behavior. Rational expressions are expanded into rational functions with vertical and horizontal asymptotes, domain, and graphing. Real-world applications include volume and dimension for boxes, areas and length/width of rectangles, and dimensions of a right circular cone and cylinder.

TOPICS

Module 8 covers the following topics:

· Dividing polynomials

· Zeros of polynomial functions

· Rational functions

OBJECTIVES

After successfully completing Module 8, you should be able to:

MO 8.1 Divide polynomials using both long division and synthetic division. [CO 1, CO 2, CO 4]

MO 8.2 Evaluate a polynomial using the remainder theorem. [CO 1, CO 2, CO 4]

MO 8.3 Use the factor theorem, rational zero theorem, linear factorization theorem, and Decartes’ rule of signs to find the zeros of a polynomial. [CO 1, CO 2, CO 4]

MO 8.4 Solve real-world applications of polynomial and rational functions. [CO 1, CO 2, CO 4, CO 5]

MO 8.5 Identify vertical and horizontal asymptotes. [CO 1, CO 2, CO 4]

MO 8.6 Write rational functions with given characteristics. [CO 1, CO 2, CO 4]

MO 8.7 Graph rational functions. [CO 1, CO 2, CO 4]

STUDY MATERIALS

Textbook Readings

· Chapter 5, sections 5.4 through 5.6 in Abramson,

College Algebra

Additional Materials

· CK-12. (n.d.).

Long division of polynomials

. CK-12 PLIX Series.

· CK-12. (n.d.).

Oblique asymptotes: Rational functions and asymptotes

. CK-12 PLIX Series.

· CK-12. (n.d.).

Excluded values for rational expressions: Holes in rational functions

. CK-12 PLIX Series.

· CK-12. (n.d.).

Horizontal and vertical asymptotes: Rational functions

. CK-12 PLIX Series.

· Pegg, E., Jr. (2011, March 7).

Simple rational functions

. Wolfram Demonstrations Project.

· Bravo, E. (2011, March 7).

Synthetic division (Ruffini’s rule)

. Wolfram Demonstrations Project.

· Blake, S. (2011, March 7).

Polynomial long division

. Wolfram Demonstrations Project.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 5.4: exercises 5, 21, 47, 63, 67, 71

·

Section 5.5: exercises 7, 17, 27, 43, 59, 73, 79

·

Section 5.6: exercises 15, 29, 33, 37, 45, 53, 59, 75

ACTIVITIES

Module 8 has four activities. Please consult the Course Calendar for the due dates.

Technology Activity 4

This technology activity has many real-world applications. You will use Geogebra and Desmos to thoroughly investigate a fourth degree polynomial. Polynomials can be used in roller coaster rides to model curves and they can be used in road designs, buildings and other structures, polynomial regression for monthly prices of a commodity, and box design. Polynomials are also an essential tool in describing and predicting traffic patterns so appropriate traffic control measures, such as traffic lights, can be implemented. Using technology and the theorems of Chapter 5, you will determine the zeros, factor and graph the polynomial, locate all local extrema, and determine end behavior. [MO 8.1, MO 8.2, MO 8.3, MO 8.4]

Technology Activity 4

Submit Technology Activity 4 and all your graph exports to your mentor for grading.

Discussion Forum 4

at least two classmates’ responses by the date indicated in the Course Calendar.

Post your results from Technology Activity 4 and discuss what you investigated and how the technology helped you better understand all the aspects of a polynomial.

When replying to your classmates’ posts, compare your investigations and how the technology helped you better understand polynomials. Note any similarities and differences and add any suggestions you feel may be helpful in better understanding polynomials and if anything should be added/changed in the activity. This will not require much of your time and is more of an extension of Technology Activity 4. [MO 8.1, MO 8.2, MO 8.3, MO 8.4]

Practice Exercises 8

You have come a long way in this course. Keep doing your best with the practice exercises so you’ll finish strong. As always, this module’s exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 8.1 through MO 8.7]

Assignment sheet for Practice Exercises 8

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 8 Quiz

You are in the home stretch for this course’s quizzes. The Module 8 quiz, like all of the others, is multiple choice, open book, untimed, and unproctored. A graphing calculator is provided as a tool within the quiz. Practice using this calculator, which is also provided on your exams.

Keep thinking of quizzes as skill-building activities rather than miniature exams. Quizzes provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams.

As you know, some of the quiz problems closely resemble problems that you’ll see on your exam. The quiz feedback identifies these problems. To make sure you can solve them, review the solution video that provides step-by-step explanations. The solution video will be available the day after the quiz is due. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook. [MO 8.1 through MO 8.7]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Module 9—Exponential and Logarithmic Functions, Part 1

OVERVIEW

Welcome to Module 9, coming down the home stretch! This module explores exponential and logarithmic functions and the relationship between the two; graphing exponential and logarithmic functions and their transformations; and solving real-world applications involving exponential and logarithmic functions like the intensity of earthquakes, compound interest, investments, virus/bacteria exponential growth, and isotope decay.

TOPICS

Module 9 covers the following topics:

· Exponential functions

· Graphs of exponential functions

· Logarithmic functions

· Graphs of logarithmic functions

OBJECTIVES

After successfully completing Module 9, you should be able to:

MO 9.1 Find the equation of exponential functions. [CO 1, CO 2, CO 4]

MO 9.2 Use compound interest formulas. [CO 1, CO 2, CO 4, CO 6]

MO 9.3 Graph exponential functions and their transformations. [CO 1, CO 2, CO 3]

MO 9.4 Convert exponential form to logarithmic form and vice versa. [CO 1, CO 2, CO 4]

MO 9.5 Evaluate logarithms. [CO 1, CO 2, CO 4]

MO 9.6 Use common and natural logarithms to solve real-world applications. [CO 1, CO 2, CO 4]

MO 9.7 Graph logarithmic functions and their transformations and determine the domain. [CO 1, CO 2, CO 3]

STUDY MATERIALS

Textbook Readings

· Chapter 6, sections 6.1 through 6.4 in Abramson,

College Algebra

Additional Materials

· Khan Academy. (n.d.).

Intro to logarithms

.

· Khan Academy. (n.d.).

Evaluate logarithms

.

· Khan Academy. (n.d.).

Relationship between exponentials and logarithms

.

· Khan Academy. (n.d.).

e

and compound interest

[Video].

· Khan Academy. (n.d.).

Graphs of exponential functions

.

· Khan Academy. (n.d.).

Graphs of logarithmic functions

.

· CK-12. (n.d.).

Solving equations with exponents: Exponent interest model

. CK-12 PLIX Series.

· Beck, G. (2011, March 7).

Laws of exponents

. Wolfram Demonstrations Project.

·

Video Resources

Self-Check Exercises

Student Solutions Manual.

Do not submit your solutions to self-assessment items to your mentor. Detailed solutions to all self-check exercises are available in Moodle.

·

Section 6.1: exercises 7, 9, 15, 21, 29, 47, 53, 61, 65

·

Section 6.2: exercises 11, 25, 27, 37, 43, 47

·

Section 6.3: exercises 9, 43, 53, 65

·

Section 6.4: exercises 17, 35, 45, 49, 53

ACTIVITIES

Module 9 has two activities. Please consult the Course Calendar for the due dates.

Practice Exercises 9

Almost there! As you have been doing in each module, you will complete practice exercises to help reinforce the skills you are learning. The exercises are based on assigned sections in the textbook. Your work will help ensure you’re well prepared for future modules and other course assessments.

Click the assignment sheet link to view the practice exercises, and follow the note about preparing assignments below.

Answer all of the problems, and show all of your work. To receive full credit for your answers, you must include complete solutions. [MO 9.1 through MO 9.7]

Assignment sheet for Practice Exercises 9

A Note About Preparing Assignments

Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.

must be clear and legible.

Only use this option if you are sure that your handwriting and scanned document will be neat and easy for your mentor to read. If your mentor cannot follow your scanned, handwritten document, you will lose credit for your work.

Review the following links for assistance:

·

Write, Insert, or Change an Equation in Microsoft Word

·

Use Equations in a Google Doc

·

Google Docs Equation Tool

Module 9 Quiz

It is time for your second-to-last module quiz. Keep in mind that these are meant to be skill-building activities. They provide a low-stress opportunity to focus on each module’s key objectives, use feedback to identify your strengths and weaknesses, and practice taking assessments that look and feel similar to your exams. You are encouraged to take the quiz multiple times for additional practice; you will see some different questions each time. Your highest score will appear in the gradebook.

Now is also a good time to get a head start on your exam prep by reading the Final Exam Study Guide, located in the Assessments section of your course space. It lists all of the topics and skills you’ll need for the exam. If anything on it is unfamiliar as you study for the exam, be sure to review your textbook, re-watch the quiz solution videos, or speak with your mentor.

The quiz consists of multiple-choice problems focusing on what you’re learning in the module. It is open book, untimed, and unproctored. A graphing calculator is provided within the quiz. Practice using this calculator, which will also be provided on your exams. [MO 9.1 through MO 9.7]

Copyright © 2022 by Thomas Edison State University. All rights reserved.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 1

SECTION 1.1

For the following exercises, simplify the given expression.

1.

2.

For the following exercise, evaluate the expression using the given variable.

3. for

a = -2

For the following exercises, simplify the expression.

4.

5.

For the following exercise, consider this scenario: Fred earns $40 at the community garden. He spends $10 on a streaming subscription, puts half of what is left in a savings account, and gets another $5 for walking his neighbor’s dog.

6. How much money does Fred keep? Show all the work.

SECTION 1.2

For the following exercise, express the number in scientific notation.

7. The average distance between Earth and the Sun is 92,960,000 mi.

For the following exercise, convert the number in scientific notation to standard notation.

8. To reach escape velocity, a rocket must travel at the rate of ft/min.

For the following exercises, simplify the given expression. Write answers with positive exponents.

9.

10.

SECTION 1.3

For the following exercises, simplify each expression.

11.

12.

For the following exercises, simplify each expression.

13.

14.

Real-World Application

15. A plane accelerates at a rate of where

t is the time in seconds after the plane moves from rest. Simplify the expression.

This work, “Practice Exercises 1,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 1” is licensed under CC BY 4.0 by Thomas Edison State University.

practice exercises_22sep/practice exercises 10_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Practice Exercises 10

SECTION 6.5

Algebraic

For the following exercise, condense to a single logarithm if possible.

1. .

For the following exercise, use the properties of logarithms to expand the logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs.

2.

For the following exercise, condense the expression to a single logarithm using the properties of logarithms.

3.

Numeric

For the following exercise, use properties of logarithms to evaluate without using a calculator.

4.

For the following exercise, use the change-of-base formula to evaluate the expression as a quotient of natural logs. Use a calculator to approximate each to five decimal places.

5.

SECTION 6.6

Algebraic

For the following exercise, use like bases to solve the exponential equation.

6. .

For the following exercise, use logarithms to solve.

7. .

For the following exercise, use the definition of a logarithm to solve the equation.

8. .

For the following exercise, use the one-to-one property of logarithms to solve.

9.

For the following exercise, solve the equation for

x.

10. .

Graphical

For the following exercise, solve the equation for x if there is a solution. Then graph both sides of the equation, and observe the point of intersection (if it exists) to verify the solution.

11. .

Technology

For the following exercise, solve the equation by rewriting the exponential expression using the indicated logarithm. Then use a calculator to approximate the variable to 3 decimal places.

12. using the common log.

For the following exercise, use a calculator to solve the equation. Round the answer to the nearest ten-thousandth.

13. Atmospheric pressure in pounds per square inch is represented by the formula , where

x is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of pounds per square inch? (Hint: There are 5280 feet in a mile.)

SECTION 6.7

Numeric

For the following exercise, use the logistic growth model

14. Find and interpret . Round to the nearest tenth.

Technology

For the following exercise, enter the data from the table into a graphing calculator and graph the resulting scatter plot. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.

15.

x

f(x)

1.25

5.75

2.25

8.75

3.56

12.68

4.2

14.6

5.65

18.95

6.75

22.25

7.25

23.75

8.6

27.8

9.25

29.75

10.5

33.5

For the following exercise, use a graphing calculator and this scenario: The population of a fish farm in years is modeled by the equation

16. To the nearest whole number, what will the fish population be after 2 years?

Real-World Applications

For the following exercise, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day.

17. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days. Round to the nearest tenth of a gram.

For the following exercise, use this scenario: A pot of warm soup with an internal temperature of 100͑° Fahrenheit was taken off the stove to cool in a 69°F room. After fifteen minutes, the internal temperature of the soup was 95°F.

18. Use Newton’s Law of Cooling to write a formula that models this situation.

For the following exercise, use this scenario: The equation models the number of people in a town who have heard a rumor after t days.

19. As increases without bound, what value does

N(t) approach? Interpret your answer.

SECTION 6.8

x

1

2

3

4

5

6

f(x)

1125

1495

2310

3294

4650

6361

20. Use a graphing calculator/utility to create a scatter diagram of the data. Use the regression feature to find an exponential function that best fits the data in the table. Write the exponential function as an exponential equation with base .

x

1

2

3

4

5

6

f(x)

5.1

6.3

7.3

7.7

8.1

8.6

21. Use the LOGarithm option of the REGression feature to find a logarithmic function of the form that best fits the data in the table. Use the logarithmic function to find the value of the function when .

This work, “Practice Exercises 10,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 10” is licensed under CC BY 4.0 by Thomas Edison State University.

practice exercises_22sep/practice exercises 2_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Practice Exercises 2

SECTION 2.1

For the following exercise, find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept.

1.

For the following exercise, solve the equation for y in terms of x.

2.

For the following exercise, find the distance between the two points. Simplify your answer, and write the exact answer in simplest radical form for irrational answers.

3.

For the following exercise, find the coordinates of the midpoint of the line segment that joins the two given points.

4.

For the following exercise, plot the three points on the given coordinate plane. Draw a line between the two endpoints and state whether the three points you plotted appear to be collinear (on the same line).

5.

For the following exercise, construct a table and graph the equation by plotting at least three points.

6.

For the following exercise, find and plot the x- and y-intercepts, and graph the straight line based on those two points.

7.

Technology

For the following exercise, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2nd CALC button and 1:value button, hit enter. At the lower part of the screen you will see “x=” and a blinking cursor. You may enter any number for x and it will display the y value for any x value you input. Use this and plug in x = 0, thus finding the y-intercept, for each of the following graphs.

If you are using the

Desmos calculator

, then enter the equation. The graphed line will appear in the coordinate plane. You will see two dots representing the

x and

y intercepts. Place your cursor over the dot representing the

y intercept and write down the order pair.

8. .

SECTION 2.2

For the following exercise, solve the equation for

x.

9.

For the following exercise, solve each rational equation for

x. State all x-values that are excluded from the solution set.

10.

For the following exercise, find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form.

11.

For the following exercise, find the equation of the line using the given information.

12. The slope is and it passes through the point

For the following exercise, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither.

13.

Numeric

For the following exercise, find the slope of the line that passes through the given points.

14.

For the following exercise, find the slope of the lines that pass through each pair of points and determine whether the lines are parallel or perpendicular.

15. ;

SECTION 2.3

Real-World Applications

For the following exercise, use the information to find a linear algebraic equation model to use to answer the question being asked.

16. Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?

For the following exercise, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.10/min for calls.

17. Find the model of the total cost of Company B’s plan, using

m for the minutes.

For the following exercise, use this scenario: A retired woman has $50,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%.

18. Let

x be the amount the woman invests in the15% bond, and 50,000 –

x the amount the woman invests in the CD. Set up and solve the equation for how much the woman should invest in each option to sustain a $6,000 annual return.

For the following exercise, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $75/wk plus $.10/mi driven. Plan B charges $100/wk plus $.05/mi driven.

19. Write the model equations for the cost of renting a truck with plan A.

For the following exercise, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

20. Use the formula to find the radius of a cylinder with a height of 36 and a volume of

This work, “Practice Exercises 2,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 2” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 3

SECTION 2.4

For the following exercise, evaluate the algebraic expression.

1. If , evaluate

y given .

Graphical

For the following exercise, plot the complex numbers on the complex plane.

.

2.

Numeric

For the following exercises, perform the indicated operation and express the result as a simplified complex number.

3.

4.

Technology

For the following exercise, use a calculator to help answer the question.

5. Evaluate for . Predict the value if

Extensions

For the following exercise, evaluate the expression, writing the result as a simplified complex number.

6.

SECTION 2.5

For the following exercise, solve the quadratic equation by factoring

7.

For the following exercise, solve the quadratic equation by using the square root property.

8.

For the following exercise, solve the quadratic equation by completing the square. Show each step.

9.

For the following exercise, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve.

10.

Technology

For the following exercise, enter the expressions into your graphing utility and find the zeros to the equation (the x-intercepts) by using 2nd CALC 2:zero. Recall finding zeros will ask left bound (move your cursor to the left of the zero, enter), then right bound (move your cursor to the right of the zero, enter), then guess (move your cursor between the bounds near the zero, enter). Round your answers to the nearest thousandth.

If you are using the

Desmos calculator

, then enter the first equation and press the ENTER key on your keyboard to get to #2. Enter the 2nd equation. The graphed quadratic and horizontal line will appear in the coordinate plane. You will see two dots representing the two points of intersection. Place your cursor over the dots representing the two solutions (points of intersection) and write down the order pairs.

11. To solve the quadratic equation we can graph these two equations

and and find the points of intersection. Recall 2nd CALC 5:intersection. If you are using the Desmos calculator, then refer to the steps above. Do this and find the solutions to the nearest tenth.

Extensions

12. Abercrombie and Fitch stock had a price given as , where the time in months is from 1999 to 2001 ( is January 1999). Find the two months in which the price of the stock was $30.

SECTION 2.7

Algebraic

For the following exercises, solve the inequality or absolute value inequality. Write your final answer in interval notation.

13.

14.

15.

16.

For the following exercise, describe all the x-values within or including a distance of the given values.

17. Distance of 10 units from the number 4.

For the following exercise, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation.

18.

Graphical

For the following exercise, graph the function. Observe the point of intersection and shade the x-axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.

19.

Numeric

For the following exercise, write the set in interval notation.

20.

For the following exercise, write the interval in set-builder notation.

21.

For the following exercise, write the set of numbers represented on the number line in interval notation.

22.

This work, “Practice Exercises 3,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 3” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 4

SECTION 3

.1

For the following exercise, determine whether the relation represents

y as a function of

x.

1.

For the following exercise, evaluate .

.

2.

Graphical

For the following exercise, use the vertical line test to determine which graphs show relations that are functions.

3.

4. Given the following graph:

a. Evaluate

b. Solve for

For the following exercise, determine if the given graph is a one-to-one function.

5.

Numeric

For the following exercise, determine whether the relation represents a function.

6.

For the following exercise, determine if the relation represented in table form represents

y as a function of

x.

7.

x

5

10

15

y

3

8

8

For the following exercise, evaluate the function

f at the values .

8.

For the following exercise, graph on the given domain. Determine the corresponding range. Show the graph.

9.

Real-World Applications

10. The amount of garbage produced by a city with population is given by is measured in tons per week, and population is measured in thousands of people.

a. The town of Tola has a population of 40,000 and produces 13 tons of

garbage each week. Express this information in terms of the function

f.

b. Explain the meaning of the statement

SECTION 3.2

For the following exercise, find the domain of the function using interval notation.

11.

Graphical

For the following exercise, write the domain and range of the function using interval notation.

12.

For the following exercise, sketch a graph of the piecewise function. Write the domain in interval notation.

13.

For the following exercise, given the function

f, evaluate

14.

For the following exercise, write the domain for the piecewise function in interval notation.

15.

SECTION 3.3

For the following exercise, find the average rate of change of the function on the interval specified for real numbers

b or

h in simplest form.

16.

For the following exercise, consider the graph of

f shown below.

17. Estimate the average rate of change from to to .

For the following exercise, use the graph of the function to estimate the intervals on which the function is increasing or decreasing.

18.

Numeric

19. The table below gives the annual sales (in millions of dollars) of a product from 1998 to

2006.

Year

1998

1999

2000

2001

2002

2003

2004

2005

2006

Sales (millions of dollars)

201

219

233

243

249

251

249

243

233

What was the average rate of change of annual sales

a. Between 2001 and 2002?

b. Between 2001 and 2004?

For the following exercise, find the average rate of change of the function on the interval specified.

20.

Technology

For the following exercise, use a graphing utility to estimate the local extrema of the function and to estimate the intervals on which the function is increasing and decreasing.

21.

Real-World Applications

22. At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125. Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?

SECTION 3.4

For the following exercise, determine the domain for the function in interval notation.

23. Given find

f +

g,

f –

g,

fg,

For the following exercise, use the pair of functions to find

f(g(x)) and

g(f(x)). Simplify your answer.

24.

For the following exercise, use the set of functions to find

f(g(h(x))). Simplify your answer.

25.

For the following exercise, find functions

f(x) and

g(x) so the given function can be expressed as

h(x)=f(g(x).

26.

Graphical

For the following exercise, use the graphs of

f shown in Figure 1 and

g shown in Figure 2 to evaluate the expression.

Figure 1

Figure 2

27.

For the following exercise, use graphs of

f(x) shown in Figure 3,

g(x) shown in Figure 4, and

h(x) shown in Figure 5 to evaluate the expression.

Figure 3

Figure 4

Figure 5

28.

For the following exercise, use the function values for

f and

g shown in the table below to evaluate the expression.

x

f(x)

g(x)

-3

11

-8

-2

9

-3

-1

7

0

0

5

1

1

3

0

2

1

-3

3

-1

-8

29.

For the following exercise, use the pair of functions to find

f(g(0)) and

g(f(0)).

30.

Real-World Applications

31. A store offers customers a 30% discount on the price

x of selected items. Then, the store takes off an additional 15% at the cash register. Write a price function

P(x) that computes the final price of the item in terms of the original price

x. (Hint: Use function composition to find your answer.)

This work, “Practice Exercises 4,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 4” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 5

SECTION 3.5

Algebraic

For the following exercise, write a formula for the function obtained when the graph is shifted as described.

1. is shifted down 4 units and to the right 3 units.

For the following exercise, describe how the graph of the function is a transformation of the graph of the original function

f.

2.

Graphical

For the following exercise, use the graph of shown in the figure below to sketch a graph of the transformation of the

f(x).

3.

For the following exercise, sketch a graph of the function as a transformation of the graph of one of the toolkit functions.

4.

For the following exercise, write an equation for the graphed function by using transformations of the graphs of one of the toolkit functions.

5.

For the following exercise, use the graph of the transformed toolkit function to write a formula for the resulting function.

6.

For the following exercise, determine whether the function is odd, even, or neither.

7.

f.

8.

For the following exercise, write a formula for the function that results when the graph of a given toolkit function is transformed as described.

9. The graph of is vertically stretched by a factor of 8, then shifted to the right 4 units and up 2 units.

For the following exercise, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.

10.

SECTION 4.1

For the following exercise, determine whether the equation of the curve can be written as a linear function.

11.

For the following exercise, determine whether the function is increasing or decreasing.

12.

For the following exercise, find the slope of the line that passes through the two given points.

13.

For the following exercise, find a linear equation satisfying the conditions, if possible.

14.

For the following exercise, determine whether the lines given by the equations are parallel, perpendicular, or neither

15.

For the following exercise, find the x- and y-intercepts of the equation.

16.

For the following exercise, use the descriptions of the pair of lines to find the slopes of Line 1 and Line 2. Is the pair of lines parallel, perpendicular, or neither?

17. Line 1: Passes through (1,7) and (5,5). Line 2: Passes through (-1,-3) and (1,1)

For the following exercise, write an equation for the line described.

18. Write an equation for a line perpendicular to and passing through the point (-4,-1).

For the following exercise, write an equation for the line graphed.

19.

For the following exercise, sketch a line with the given features.

20. A

y-intercept of (0,5) and slope .

For the following exercise, write the equation of the line shown in the graph.

21.

SECTION 4.2

For the following exercise, consider this scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped to 4,700. Assume this trend continues.

22. Identify the year in which the population will reach 0.

For the following exercise, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted.

23. Find a reasonable domain and range for the function.

Real-World Applications

24. In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured to be 285. The population changed linearly. Let the input be years since 2003.

a. Find a formula for the owl population,

P. Let the input be years since 2003.

b. What does your model predict the owl population to be in 2012?

25. When hired at a new job selling electronics, you are given two pay options:

Option A: Base salary of $10,000 a year with a commission of 9% of your sales.

Option B: Base salary of $19,000 a year with a commission of 4% of your sales.

Write a model for each option. How much would you need to sell for option A to produce a larger income?

SECTION 4.3

For the following exercise, draw a scatter plot for the data provided. Does the data appear to be linearly related?

26.

100

250

300

450

600

750

12

12.6

13.1

14

14.5

15.2

For the following exercise, draw a best-fit line for the plotted data.

27.

Numeric

28. The U.S. Census tracks the percentage of persons 25 years or older who are college graduates. That data for several years is given in the table below. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the percentage exceed 35%?

Year

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

Percent Graduates

21.3

21.4

22.2

23.6

24.4

25.6

26.7

27.7

28

29.4

For the following exercise, consider this scenario: The population of a city increased steadily over a 10-year span. The following ordered pairs shows the population and the year over the 10-year span (population, year) for specific recorded years:

29. Use linear regression to determine a function,

y, where the year depends on the population. Round to three decimal places of accuracy. Predict when the population will hit 8,000.

This work, “Practice Exercises 5,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 6

SECTION 1.4

For the following exercise, identify the degree of the polynomial.

1.

For the following exercise, find the sum or difference.

2.

For the following exercise, find the product.

3.

For the following exercise, expand the binomial.

4.

For the following exercise, multiply the binomials.

5.

For the following exercise, multiply the polynomials.

6.

SECTION 1.5

For the following exercise, find the greatest common factor.

7.

For the following exercise, factor by grouping.

8.

For the following exercise, factor the polynomial.

9.

For the following exercise, factor the polynomials.

10.

For the following exercise, consider the following scenario:

A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yd. as shown in the figure below. The flagpole will take up a square plot with area .

11. Find the length of the base of the flagpole by factoring.

SECTION 1.6

For the following exercise, simplify the rational expression.

12.

For the following exercise, multiply the rational expressions and express the product in simplest form.

13.

For the following exercise, divide the rational expressions.

14.

For the following exercise, add and subtract the rational expressions, and then simplify.

15.

For the following exercise, simplify the rational expression.

16.

Real-World Applications

17. The area of Lijuan’s yard is ft2. A patch of sod has an area of ft2. Divide the two areas and simplify to find how many pieces of sod Lijuan needs to cover her yard.

This work, “Practice Exercises 6,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 6” is licensed under CC BY 4.0 by Thomas Edison State University.

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MAT-121: COLLEGE ALGEBRA

Practice Exercises 7

SECTION 5

.1

Algebraic

For the following exercise, rewrite the quadratic function in standard form and give the vertex. Determine whether there is a minimum or maximum value to the quadratic function. Find

the value and the axis of symmetry. Determine the domain and range.

1.

For the following exercise, use the vertex and a point on the graph to find the general form of the equation of the quadratic function.

2.

Graphical

For the following exercise, sketch a graph of the quadratic function and give the vertex, axis of symmetry, and intercept.

3.

For the following exercise, write the equation for the graphed quadratic function.

4.

Numeric

For the following exercise, use the table of values that represent points on the graph of a quadratic function. By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.

5.

x

-2

-1

0

1

2

y

8

2

0

2

8

Technology

For the following exercise, use a calculator or graphing utility to find the answer.

6. Graph on the same set of axes

.

What appears to be the effect of adding a constant?

SECTION 5.2

Algebraic

For the following exercise, identify the function as a power function, a polynomial function, or neither. If the function is polynomial then find the degree and leading coefficient for the given polynomial.

7.

For the following exercise, determine the end behavior of the function and find the intercepts of the function.

8.

Graphical

For the following exercise, determine the least possible degree of the polynomial function shown.

9.

Technology

For the following exercise, graph the polynomial function using a calculator or graphing utility. Based on the graph, determine the intercepts and the end behavior.

10.

Extensions

For the following exercise, use the information about the graph of a polynomial function to determine the function. Assume the leading coefficient is 1 or –1. There may be more than one correct answer.

11. The

y-intercept is (0,9). The

x-intercepts are (-3,0), (3,0). Degree is 2.

Real-World Applications

For the following exercise, use the written statements to construct a polynomial function that represents the required information.

12. An oil slick is expanding as a circle. The radius of the circle is increasing at the rate of 20 meters per day. Express the area of the circle as a function of the number of days elapsed. The area of a circle is and the diameter is twice the radius.

SECTION 5.3

Algebraic

For the following exercise, find the or t-intercepts of the polynomial functions.

13.

Graphical

For the following exercises, graph the polynomial functions. Note

y-intercept, all zeros and their multiplicity, and end behavior.

14.

For the following exercise, use the graph to write the formula for a polynomial function of least degree. Identify zeros and their multiplicity.

15.

For the following exercise, use the given information about the polynomial graph to write the equation.

16. Degree 3. Zeros at .

y-intercept at .

Technology

For the following exercise, use a calculator to approximate local minima and maxima or the global minimum and maximum.

17.

Real-World Applications

For the following exercise, write the polynomial function that models the given situation.

18. A cylinder has a radius of units and a height of 3 units greater. Express the volume of the cylinder as a polynomial function. The volume of a cylinder is .

This work, “Practice Exercises 7,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 7” is licensed under CC BY 4.0 by Thomas Edison State University.

image1

image2

image3

practice exercises_22sep/practice exercises 8_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Practice Exercises 8

SECTION 5.4

Algebraic

For the following exercise, use long division to divide. Specify the quotient and the remainder.

1.

For the following exercise, use synthetic division to find the quotient. Ensure the equation is in the form required by synthetic division. (Hint: Divide the dividend and divisor by the coefficient of the linear term in the divisor. Make sure the coefficient for the divisor is 1.)

2.

Graphical

For the following exercise, use the graph of the third-degree polynomial and one factor to write the factored form of the polynomial suggested by the graph. The leading coefficient is 1.

3. Factor is

Extensions

For the following exercise, use synthetic division to determine the quotient involving a complex number.

4.

Real-World Applications

For the following exercise, use the given volume of a box and its length and width to express the height of the box algebraically.

5. Volume is , length is , width is .

For the following exercise, use the given volume and radius of a cylinder to express the height of the cylinder algebraically.

6. Volume is , radius is .

SECTION 5.5

Algebraic

For the following exercise, use the Remainder Theorem to find the remainder.

7.

For the following exercise, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.

8.

For the following exercise, use the Rational Zero Theorem to find the real solution(s) to the equation.

9. .

For the following exercise, find the complex solutions (real and non-real).

10.

Numeric

For the following exercise, list all possible rational zeros for the function.

11.

Real-World Applications

For the following exercise, find the dimensions of the box described.

12. The length is 3 times the height and the height is 1-inch less than the width. The volume is 108 cubic inches.

For the following exercise, find the dimensions of the right circular cylinder described.

13. The radius and height differ by 1 meter. The radius is larger and the volume is cubic meters.

SECTION 5.6

Algebraic

For the following exercise, find the domain, vertical asymptote, and horizontal asymptote of the function.

14.

For the following exercise, describe the local and end behavior of the function.

15.

For the following exercise, find the slant asymptote of the function.

16.

Graphical

For the following exercise, use the given transformation to graph the function. Note the vertical and horizontal asymptotes.

17. The reciprocal squared function shifted down 2 units and right 1 unit.

Graphical

For the following exercise, find the horizontal intercept, the vertical intercept, the vertical asymptote, and the horizontal or slant asymptote of the function. Use that information to sketch a graph.

18.

For the following exercise, write an equation for a rational function with the given characteristics.

19. Vertical asymptotes at ,

x-intercepts at (-2,0) and (1,0). Horizontal asymptote at .

For the following exercise, use the graph to write an equation for the function.

20.

Extensions

For the following exercise, identify the removable discontinuity.

21.

This work, “Practice Exercises 8,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 8” is licensed under CC BY 4.0 by Thomas Edison State University.

image2

image1

practice exercises_22sep/practice exercises 9_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Practice Exercises 9

SECTION 6

.1

Algebraic

For the following exercise, identify whether the statement represents an exponential function. Explain.

1. The height of a projectile at time is represented by the function .

For the following exercise, consider this scenario: For each year the population of a forest of trees is represented by the function In a neighboring forest, the population of the same type of tree is represented by the function (Round answers to the nearest whole number.)

2. Which forest had a greater number of trees initially? By how many?

For the following exercise, determine whether the equation represents exponential growth, exponential decay, or neither. Explain.

3.

For the following exercise, find the formula for an exponential function that passes through the two points given.

4.

For the following exercise, use the compound interest formula, .

5. After a certain number of years, the value of an investment account is represented by the equation What is the value of the account?

Numeric

For the following exercise, evaluate each function. Round answers to four decimal places, if necessary.

6. , for

Technology

For the following exercise, use a graphing calculator to find the equation of an exponential function given the points on the curve.

7. .

Real-World Applications

8. A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After 35 hours, 50 mg of the substance remains. How many milligrams will remain after 54 hours?

9. Kyoko has $10,000 that she wants to invest. Her bank has several investment accounts to choose from, all compounding daily. Her goal is to have $15,000 by the time she finishes graduate school in 6 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal? (Hint: Solve the compound interest formula for the interest rate. Note: banks use 360 for

n when compounded daily.)

SECTION 6.2

For the following exercise, graph each set of functions on the same axes.

10. .

For the following exercise, graph the function and its reflection about the x-axis on the same axes.

11.

For the following exercise, graph the transformation of Give the horizontal asymptote, the domain, and the range and describe the end behavior.

12. .

For the following exercise, start with the graph of Then write a function that results from the given transformation.

13. Reflect about the

x axis.

Numeric

For the following exercise, evaluate the exponential function for the indicated value of

x.

14. .

Technology

For the following exercise, use a graphing calculator to approximate the solution of the equation. Round to the nearest thousandth.

15. .

SECTION 6.3

Algebraic

For the following exercise, rewrite the log equation in exponential form and the exponential equation in logarithmic form.

16.

Numeric

For the following exercise, evaluate the base logarithmic expression without using a calculator.

17.

For the following exercise, evaluate the natural logarithmic expression without using a calculator.

18.

Real-World Applications

19. The exposure index for a camera is a measurement of the amount of light that hits the image receptor. It is determined by the equation where

f is the “f-stop” setting on the camera, and

t is the exposure time in seconds. Suppose the f-stop setting is and the desired exposure time is seconds. What will the resulting exposure index be?

SECTION 6.4

Algebraic

For the following exercise, state the domain, vertical asymptote, and end behavior of the function.

20.

Graphical

For the following exercise, sketch the graphs of the pair of functions on the same axis.

21.

For the following exercise, sketch the graph of the indicated function.

22.

For the following exercise, write a logarithmic equation corresponding to the graph shown.

23. Use as the parent function.

Technology

For the following exercise, use a graphing calculator to find an approximate solution to the equation.

24.

This work, “Practice Exercises 9,” is a derivative of

College Algebra 2e by Jay Abramson, OpenStax used under

CC BY 4.0. “Practice Exercises 9” is licensed under CC BY 4.0 by Thomas Edison State University.

image1

resources_22sep/1.1 – 1.3 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 1.1–1.3

SECTION 1.1—

REAL NUMBERS: ALGEBRA ESSENTIALS

Sets of Real Numbers

Mathispower4u. (2011, October 17).

Identifying sets of real numbers

[Video]. YouTube.

Determine Rational or Irrational Numbers (Square Roots and Decimals Only)

Mathispower4u. (2017, June 23).

Determine rational or irrational numbers (square roots and decimals only)

[Video]. YouTube.

Order of Operations

Mathispower4u. (2014, August 11).

Order of operations (L1.1)

[Video]. YouTube.

Properties of Real Numbers

Mathispower4u. (2016, July 1).

Properties of real numbers

[Video]. YouTube.

Evaluating Algebraic Expressions

Mathispower4u. (2011, March 30).

Evaluating algebraic expressions

[Video]. YouTube.

Circumference, Volume of a Cone, Pythagorean Theorem

Mathispower4u. (2015, April 20).

Circumference, volume of a cone, Pythagorean Theorem (L1.5)

[Video]. YouTube.

Simplifying Algebraic Expressions

Mathispower4u. (2009, August 31).

Simplifying algebraic expressions

[Video]. YouTube.

SECTION 1.2—EXPONENTS AND SCIENTIFIC NOTATION

Simplify Expressions Using the Product Rule of Exponents

Mathispower4u. (2016, July 12).

Simplify expressions using the product rule of exponents (basic)

[Video]. YouTube.

Simplify Expressions Using the Quotient Rule of Exponents

Mathispower4u. (2016, July 12).

Simplify expressions using the quotient rule of exponents (basic)

[Video]. YouTube.

Simplify Expressions Using the Power Rule of Exponents

Mathispower4u. (2016, July 12).

Simplify expressions using the power rule of exponents (basic)

[Video]. YouTube.

Evaluate and Simplify Expressions Using the Zero Exponent Rule

Mathispower4u. (2016, May 30).

Evaluate and simplify expressions using the zero exponent rule

[Video]. YouTube.

Simplify Basic Expressions with Negative Exponents

Mathispower4u. (2017, August 3).

Simplify basic expressions with negative exponents: -8^(-3), (-8)^(-3), 5y^(-1), (5y)^(-1)

[Video]. YouTube.

Simplify Expressions Using Exponent Rules (Power of a Product)

Mathispower4u. (2016, July 13).

Simplify expressions using exponent rules (power of a product)

[Video]. YouTube.

Simplify Expressions Using Exponent Rules (Power of a Quotient)

Mathispower4u. (2016, July 13).

Simplify expressions using exponent rules (power of a quotient)

[Video]. YouTube.

Simplify Exponential Expressions—Positive Exponents Only

Mathispower4u. (2011, October 1).

Ex 1: Simplify exponential expressions – Positive exponents only

[Video]. YouTube.

Scientific Notation

Mathispower4u. (2009, November 2).

Scientific notation

[Video]. YouTube.

Application of Scientific Notation—Quotient 1 (Number of Times Around the Earth)

Mathispower4u. (2016, May 31).

Application of scientific notation – quotient 1 (number of times around the earth)

[Video]. YouTube.

SECTION 1.3—RADICAL AND RATIONAL EXPONENTS

Introduction to Square Roots

Mathispower4u. (2010, November 12).

Introduction to square roots

[Video]. YouTube.

Simplifying square-root expressions

Khan Academy. (2017, March 30).

Simplifying square-root expressions | Mathematics I | High School Math | Khan Academy

[Video]. YouTube.

Adding and Subtracting Radicals

Mathispower4u. (2010, July 9).

Adding and subtracting radicals

[Video]. YouTube.

Rationalize the Denominator—Square Root with Variable

Mathispower4u. (2018, April 17).

Rationalize the denominator – square root with variable

[Video]. YouTube.

Rationalize the Denominator of a Radical Expression—Conjugate

Mathispower4u. (2011, November 18).

Ex: rationalize the denominator of a radical expression – conjugate

[Video]. YouTube.

Simplify Nth Roots with Variables

Mathispower4u. (2016, August 4).

Simplify nth roots with variables

[Video]. YouTube.

Write Rational Exponents as Radicals and Radicals Using Rational Exponents (Variables)

Mathispower4u. (2018, April 14).

Write rational exponents as radicals and radicals using rational exponents (variables)

[Video]. YouTube.

Simplify Expressions with Rational Exponents

Mathispower4u. (2011, November 16).

Ex: Simplify expressions with rational exponents

[Video]. YouTube.

resources_22sep/1.4 – 1.6 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 1.4–1.6

SECTI

ON 1.4

—POLYNOMIALS

Coefficient and Degree

Mathispower4u. (2009, November 2).

Introduction to polynomials

[Video]. YouTube.

Adding and Subtracting

Mathispower4u. (2014, August 10).

Adding and subtracting polynomials (l3.2)

[Video]. YouTube.

Multiplying

Mathispower4u. (2010, July 14).

Multiplying polynomials

[Video]. YouTube.

Khan Academy. (2019, July 24).

Multiplying monomials | Polynomial arithmetic | Algebra 2 | Khan Academy

[Video]. YouTube.

Khan Academy. (2020, February 10).

Area model for multiplying polynomials with negative terms

[Video]. YouTube.

Mathispower4u. (2009, November 5).

Special polynomial products

[Video]. YouTube.

Using Distributive Property

Mathispower4u. (2011, October 4).

Ex: Multiplying using the distributive property

[Video]. YouTube.

Mathispower4u. (2019, May 13).

Multiplying binomials and trinomials

[Video]. YouTube.

1.5 FACTORING POLYNOMIALS

Greatest Common Factor (GCF)

Mathispower4u. (2015, September 21).

Ex: Determine the GCF of two monomials (two variables)

[Video]. YouTube.

Mathispower4u. (2017, August 3).

Factor the GCF from a trinomial: 30x^3-36x^2+12x

[Video]. YouTube.

Trinomials, Leading Coefficient of 1

Mathispower4u. (2011, October 12).

Ex: Factor trinomials when a equals 1

[Video]. YouTube.

Mathispower4u. (2019, February 4).

Using the TI84 table to help factor trinomials with a = 1

[Video]. YouTube.

Trinomials, Leading Coefficient Not 1

Mathispower4u. (2011, October 12).

Ex: Factor trinomials when a is not equal to 1 – trial and error method

[Video]. YouTube.

Mathispower4u. (2011, October 12).

Ex: Factor trinomials when a is not equal to 1 – bottoms up method

[Video]. YouTube.

Factor by Grouping

Mathispower4u. (2014, December 14).

Ex 1: Factor a quadratic expression using grouping

[Video]. YouTube.

Perfect Square

Mathispower4u. (2010, November 23).

Factoring a perfect square trinomial

[Video]. YouTube.

Difference of Squares

Mathispower4u. (2010, November 23).

Factoring a difference of squares

[Video]. YouTube.

Sum/Difference of Cubes

Mathispower4u. (2010, July 8).

Factoring a sum or difference of cubes

[Video]. YouTube.

Factoring Expressions With Fractional or Negative Exponents

Mathispower4u. (2016, July 21).

Factor expressions with negative exponents

[Video]. YouTube.

Mathispower4u. (2016, July 21).

Factor expressions with fractional exponents

[Video]. YouTube.

1.6 RATIONAL EXPRESSIONS

Simplifying Rational Expressions

Mathispower4u. (2010. July 8).

Simplifying rational expressions

[Video]. YouTube.

Mathispower4u. (2016, June 22).

Simplify and give the domain of rational expressions

[Video]. YouTube.

Mathispower4u. (2011, December 8).

Ex 3: Simplify rational expressions

[Video]. YouTube.

Multiplying Rational Expressions

Mathispower4u. (2011, December 12).

Ex 1: Multiply rational expressions – monomials

[Video]. YouTube.

Mathispower4u. (2011, December 12).

Ex 4: Multiply rational expressions

[Video]. YouTube.

Dividing Rational Expressions

Mathispower4u. (2011, December 12).

Ex 1: Dividing rational expressions – monomials

[Video]. YouTube.

Mathispower4u. (2011, December 12).

Ex 2: Dividing rational expressions

[Video]. YouTube.

Adding and Subtracting Rational Expressions

Mathispower4u. (2016, June 22).

Add and subtract rational expressions with like denominators and give the domain

[Video]. YouTube.

Mathispower4u. (2018, April 10).

Add or subtract basic rational expressions with unlike denominators

[Video]. YouTube.

Mathispower4u. (2011, December 13).

Ex: Add and subtract rational expressions – opposite denominators

[Video]. YouTube.

Simplifying Complex Rational Expressions

Mathispower4u. (2012, November 9).

Ex 2: Simplify a complex fraction (variables)

[Video]. YouTube.

Mathispower4u. (2015, September 29).

Ex: Simplify a complex fraction with addition and subtraction and constant denominators

[Video]. YouTube.

resources_22sep/2.1 – 2.3 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 2.1–2.3

SECTION 2.1

—THE RECTANGULAR COORDINATE SYSTEM AND GRAPHS

Plotting Ordered Pairs in the Cartesian Coordinate System

Khan Academy. (2012, February 15).

Introduction to the coordinate plane | Introduction to algebra | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2014, August 14).

Introduction to the cartesian plane – Part 1 (L8.1A)

[Video]. YouTube.

Mathispower4u. (2011, September 12).

Identify the quadrant of a point on the coordinate plane

[Video]. YouTube.

Graphing Equations by Plotting Points

Mathispower4u. (2009, June 10).

Graphing equations by plotting points – Part 2

[Video]. YouTube.

Mathispower4u. (2015, April 14).

Graphing by plotting points – linear (l6.3)

[Video]. YouTube.

Graphing Equations with a Graphing Utility

Mathispower4u. (2010, October 5).

Graphing lines on the TI83 or TI84

[Video]. YouTube.

Finding x-Intercepts and y-Intercepts

Khan Academy. (2015, April 21).

Introduction to intercepts | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2016, May 1).

Graph linear equations using intercepts

[Video]. YouTube.

Mathispower4u. (2018, February 22).

Interpret the meaning of the intercepts of a graph (sales and profit)

[Video]. YouTube.

Khan Academy. (2013, August 10).

Finding the x-intercept of a line | Algebra I | Khan Academy

[Video]. YouTube.

Using the Distance Formula

Mathispower4u. (2015, October 6).

Ex: Determine the distance between two points using the pythagorean theorem

[Video]. YouTube.

Mathispower4u. (2015, October 6).

Ex: Find the shortest distance between two locations north and west

[Video]. YouTube.

Using the Midpoint Formula

Mathispower4u. (2011, November 22).

Ex: Midpoint of a segment

[Video]. YouTube.

Mathispower4u. (2012, September 18).

Ex 1: Find standard equation of a circle given the endpoints of a diameter

[Video]. YouTube.

SECTION 2.2—LINEAR EQUATIONS IN ONE VARIABLE

Solving Linear Equations in One Variable

Mathispower4u. (2012, December 14).

Ex: Solving linear equations in one variable with parentheses

[Video]. YouTube.

Mathispower4u. (2014, August 12).

Solving multi-step equations (L5.4)

[Video]. YouTube.

Solving Rational Equations

Mathispower4u. (2010, July 8).

Solving rational equations

[Video]. YouTube.

Mathispower4u. (2016, June 23).

Solve basic rational equations

[Video]. YouTube.

Khan Academy. (2016, March 8).

Equations with rational expressions | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Finding a Linear Equation

Khan Academy. (2015, April 22).

Slope-intercept form | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2015, April 21).

Introduction to slope | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2016, January 15).

Ex: Determine the slope of a line given two points (horizontal and vertical)

[Video]. YouTube.

The Point Slope Formula

Khan Academy. (2013, August 5).

Introduction to point-slope form | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2011, September 9).

Ex: Find the equation of a line in point slope and slope intercept form given the slope and a point

[Video]. YouTube.

Mathispower4u. (2011, September 9).

Ex: Find the equation of the line in point-slope and slope intercept form given two points

[Video]. YouTube.

Standard Form

Khan Academy. (2015, April 22).

Standard form for linear equations | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2010, September 14).

Linear equations in standard form

[Video]. YouTube.

Mathispower4u. (2011, September 7).

Ex 1: Find the equation of a line in standard form given two points

[Video]. YouTube.

Vertical and Horizontal Lines

Mathispower4u. (2014, August 14).

Graphing horizontal and vertical lines (l8.6)

[Video]. YouTube.

Khan Academy. (2017, March 27).

Horizontal & vertical lines | Mathematics I | High School Math | Khan Academy

[Video]. YouTube.

Determining Whether Graphs of Lines Are Parallel or Perpendicular

Khan Academy. (2015, July 16).

Parallel and perpendicular lines intro | Analytic geometry | Geometry | Khan Academy

[Video]. YouTube.

Khan Academy. (2018, June 18).

Parallel & perpendicular lines from graph

[Video]. YouTube.

Writing the Equations of Lines Parallel or Perpendicular to a Given Line

Mathispower4u. (2010, September 21).

Parallel and perpendicular lines – Part 2

[Video]. YouTube.

Mathispower4u. (2016, May 1).

Determine the equation of a line perpendicular to a line in slope-intercept form

[Video]. YouTube.

SECTION 2.3—MODELS AND APPLICATIONS

Setting Up a Linear Equation to Solve a Real-World Application

Mathispower4u. (2016, January 17).

Ex: Write a linear equation that models cricket chirps (linear equation application)

[Video]. YouTube.

Mathispower4u. (2016, January 17).

Ex: Write a linear equation that models depreciation (linear equation application)

[Video]. YouTube.

Using a Formula to Solve a Real-World Application

Khan Academy. (2011, September 30).

Perimeter and area: the basics | Perimeter, area, and volume | Geometry | Khan Academy

[Video]. YouTube.

Mathispower4u. (2016, May 13).

Problem solving using distance, rate, time (running)

[Video]. YouTube.

Mathispower4u. (2011, December 6).

Ex: Find the size of cardboard needed to make a box with a given volume

[Video]. YouTube.

resources_22sep/2.4, 2.5, 2.7 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 2.4, 2.5, 2.7

SECTION 2.4—COMPLEX NUMBERS

Expressing Square Roots of Negative Numbers as Multiples of i

Mathispower4u. (2010, June 19).

Introduction to complex numbers

[Video]. YouTube.

Mathispower4u. (2016, August 5).

Simplify square roots to imaginary numbers

[Video]. YouTube.

Plotting a Complex Number on the Complex Plane

Khan Academy. (2013, August 14).

Plotting complex numbers on the complex plane | Precalculus | Khan Academy

[Video]. YouTube.

Adding and Subtracting Complex Numbers

Mathispower4u. (2016, August 5).

Write number in the form of complex numbers

[Video]. YouTube.

Investigation of Complex Numbers

Thomas Edison State University. (2022, July 5).

Investigation of Complex Numbers (kaltura.com)

[Video]. Kaltura.

Adding and Subtracting Complex Numbers

Mathispower4u. (2011, November 22).

Ex 1: Adding and subtracting complex numbers

[Video]. YouTube.

Mathispower4u. (2011, November 22).

Ex 2: Adding and subtracting complex numbers

[Video]. YouTube.

Mathispower4u. (2011, November 22).

Ex: Simplify, add, and subtract imaginary and complex numbers

[Video]. YouTube.

Multiplying Complex Numbers

Multiplying Complex Number by a Real Number

Mathispower4u. (2011, November 23).

Ex 1: Simplify and multiply complex numbers

[Video]. YouTube.

Multiplying Complex Numbers Together

Mathispower4u. (2011, November 23).

Ex 2: Multiply complex numbers

[Video]. YouTube.

Mathispower4u. (2011, November 23).

Ex 3: Multiply complex numbers

[Video]. YouTube.

Mathispower4u. (2018, April 17).

Multiply three complex numbers

[Video]. YouTube.

Mathispower4u. (2018, April 17).

Cube a complex number

[Video]. YouTube.

Mathispower4u. (2019, November 8).

Simplifying powers of i (method of dividing by 4)

[Video]. YouTube.

Mathispower4u. (2011, November 23).

Ex: Raising the imaginary unit i to powers

[Video]. YouTube.

Dividing Complex Numbers

The Complex Conjugate

Khan Academy. (2011, July 12).

Complex conjugates example | Imaginary and complex numbers | Precalculus | Khan Academy

[Video]. YouTube.

Mathispower4u. (2011, November 23).

Ex: Multiplying complex conjugates

[Video]. YouTube.

Dividing Complex Numbers

Khan Academy. (2011, July 12).

Dividing complex numbers | Imaginary and complex numbers | Precalculus | Khan Academy

[Video]. YouTube.

Mathispower4u. (2011, November 23).

Ex: Dividing complex numbers

[Video]. YouTube.

Operations of Complex Number on a Graphing Calculator

Mathispower4u. (2012, November 16).

Complex number operations on the TI-84

[Video]. YouTube.

Simplifying Powers of i

Mathispower4u. (2019, November 8).

Simplifying powers of i (method of dividing by 4)

[Video]. YouTube.

Khan Academy. (2011, July 11).

Calculating i raised to arbitrary exponents | Precalculus | Khan Academy

[Video]. YouTube.

SECTION 2.5—QUADRATIC EQUATIONS

Strategy in Factoring Quadratics

Khan Academy. (2017, April 3).

Recognizing quadratic factor methods

[Video]. YouTube.

Khan Academy. (2017, April 3).

Recognizing quadratic factor methods part 2

[Video]. YouTube.

Solving Quadratic Equations by Factoring

Zero Product Property

Mathispower4u. (2011, November 2).

The Zero-product property

[Video]. YouTube.

Solving Quadratic Equations with a Leading Coefficient of 1

Mathispower4u. (2011, October 12).

Ex: Factor and solve quadratic equations when a equals 1

[Video]. YouTube.

Mathispower4u. (2011, November 2).

Ex 1: Factor and solve quadratic equation – trinomial a = 1

[Video]. YouTube.

Solving Quadratic Equations When the Leading Coefficient is not 1

Mathispower4u. (2014, December 14).

Ex: Solve a quadratic equation using factor by grouping

[Video]. YouTube.

Mathispower4u. (2011, November 4).

Ex 1: Factor and solve a quadratic equation – a not 1

[Video]. YouTube.

Solve by Using Square Root Property

Mathispower4u. (2010, July 15).

Solving quadratic equations using square roots

[Video]. YouTube.

Mathispower4u. (2011, December 2).

Ex 1: Solving quadratic equations using square roots

[Video]. YouTube.

Mathispower4u. (2011, December 2).

Ex 2: Solving quadratic equations using square roots

[Video]. YouTube.

Completing the Square

Khan Academy. (2010, April 12).

Solving quadratic equations by completing the square | Algebra II | Khan Academy

[Video]. YouTube.

Mathispower4u. (2014, December 4).

Forming perfect square trinomials

[Video]. YouTube.

Using the Quadratic Formula

Khan Academy. (2010, April 12).

How to use the quadratic formula | Polynomial and rational functions | Algebra II | Khan Academy

[Video]. YouTube.

Mathispower4u. (2018, December 7).

Solve a quadratic equation using the quadratic formula (basic complex)

[Video]. YouTube.

Mathispower4u. (2011, December 6).

Ex1: Quadratic formula – two real irrational solutions

[Video]. YouTube.

The Discriminant

Mathispower4u. (2011, December 6).

Ex: the discriminant

[Video]. YouTube.

Khan Academy. (2011, July 12).

Discriminant for types of solutions for a quadratic | Algebra II | Khan Academy

[Video]. YouTube.

Using Pythagorean Theorem

Mathispower4u. (2010, July 15).

The Pythagorean Theorem

[Video]. YouTube.

Mathispower4u. (2011, May 24).

Example: determine the length of the hypotenuse of a right triangle

[Video]. YouTube.

Mathispower4u. (2011, May 24).

Example: determine the length of the leg of a right triangle

[Video]. YouTube.

SECTION 2.7—LINEAR INEQUALITIES AND ABSOLUTE VALUE INEQUALITIES

Using Interval Notation

Mathispower4u. (2016, May 15).

Given interval in words, graph and give interval notation

[Video]. YouTube.

Mathispower4u. (2013, May 16).

Set-Builder notation

[Video]. YouTube.

Khan Academy. (2015, June 23).

Intervals and interval notation | Functions | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2014, July 9).

Ex: Express intervals using inequalities, using a graphs, an using interval notation

[Video]. YouTube.

Using the Properties of Inequalities

Khan Academy. (2010, April 7).

Inequalities using addition and subtraction | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2011, September 26).

Ex: Solving a one step linear inequality by multiplying

[Video]. YouTube.

Solving Inequalities in One Variable Algebraically

Khan Academy. (2011, July 15).

Multi-step inequalities 3 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, January 25).

Multi-step inequalities 2 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2018, March 3).

Determine the construction steps of a two step inequality

[Video]. YouTube.

Mathispower4u. (2014, August 13).

Solving linear inequalities in one variable (l7.3)

[Video]. YouTube.

Understanding Compound Inequalities

Mathispower4u. (2014, August 13).

Introduction to basic compound inequalities – AND only (l7.5)

[Video]. YouTube.

Khan Academy. (2011, January 25).

Compound inequalities | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, January 25).

Compound inequalities 2 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, January 25).

Compound inequalities 4 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, July 15).

Compound inequalities 3 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Solving Absolute Value Inequalities

Khan Academy. (2010, April 7).

Absolute value inequalities | Linear equations | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2010, June 13).

Absolute value inequalities example 1 | Linear equations | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, January 25).

Absolute value inequalities example 2 | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2010, June 13).

Absolute inequalities 2 | Linear equations | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2010, June 13).

Absolute value inequalities example 3 | Linear equations | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2010, June 13).

Writing and using inequalities | Linear inequalities | Algebra I | Khan Academy

[Video]. YouTube.

resources_22sep/3.1 – 3.4 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 3

.1–3.4

SECTION 3

.1

—FUNCTIONS AND FUNCTION NOTATION

Determining Whether a Relation Represents a Function

Mathispower4u. (2014, August 14).

Introduction to relations and functions (L9.1)

[Video]. YouTube.

Using Function Notation

Mathispower4u. (2014, August 14).

Introduction to function notation (L9.2)

[Video]. YouTube.

Mathispower4u. (2018, February 24).

Application: Determine the meaning of function values

[Video]. YouTube.

Representing Functions Using Tables

Mathispower4u. (2015, November 27).

Ex: Use a table to find function inputs and outputs – items sold application

[Video]. YouTube.

Mathispower4u. (2019, May 16).

Represent a discrete function using ordered pairs, a table, and function notation

[Video]. YouTube.

Finding Input and Output Values of a Function

Evaluation of Functions in Algebraic Forms

Khan Academy. (2013, June 4).

Evaluating functions given their formula | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Mathispower4u. (2014, August 14).

Evaluating functions using function notation (l9.3)

[Video]. YouTube.

Mathispower4u. (2018, February 24).

Determine a variety of function values

[Video]. YouTube.

Evaluating Functions Expressed in Formulas

Mathispower4u. (2013, July 15).

Ex: Find an output of a demand function

[Video]. YouTube.

Khan Academy. (2015, August 6).

How to interpret an expression with function notation | Functions | Algebra I | Khan Academy

[Video]. YouTube.

Evaluating Functions Given in Tabular Form

Mathispower4u. (2012, June 7).

Ex: Evaluate a function and solve for a function value given a table

[Video]. YouTube.

Finding Function Values From a Graph

Mathispower4u. (2011, October 17).

Ex: Given a graph and a function value, determine the input or x-value

[Video]. YouTube.

Khan Academy. (2013, June 4).

Evaluating functions given their graph | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Determining Whether a Function is One-to-One

Mathispower4u. (2012, June 6).

Determine if a relation given as a table is a one-to-one function

[Video]. YouTube.

Using the Vertical Line Test

Mathispower4u. (2012, June 6).

Ex 1: Determine if the graph of a relation is a one-to-one function

[Video]. YouTube.

Using the Horizontal Line Test

Mathispower4u. (2012, June 6).

Ex 1: Determine if the graph of a relation is a one-to-one function

[Video]. YouTube.

Mathispower4u. (2012, June 6).

Ex 2: Determine if the graph of a relation is a one-to-one function

[Video]. YouTube.

Mathispower4u. (2018, February 11).

Horizontal line test and one to one functions

[Video]. YouTube.

Identifying Basic Toolkit Functions

Mathispower4u. (2013, May 6).

Graphing 9 basic functions

[Video]. YouTube.

SECTION 3.2—DOMAIN AND RANGE

Restrictions on the Domain and Range

The Organic Chemistry Tutor. (2017, September 8).

How to find the domain of a function – Radicals, fractions & square roots – Interval notation

[Video]. YouTube.

Finding the Domain of a Function Defined by an Equation

Interval Notation

Khan Academy. (2015, June 23).

Intervals and interval notation | Functions | Algebra I | Khan Academy

[Video]. YouTube.

Mathispower4u. (2015, October 13).

Ex 1: Find domain and range of ordered pairs, function or not

[Video]. YouTube.

Mathispower4u. (2011, September 19).

Ex: Determine the domain of a rational function

[Video]. YouTube.

Using Notations to Specify Domain and Range

The Organic Chemistry Tutor. (2018, February 7).

Set builder notation and roster method

[Video]. YouTube.

Mathispower4u. (2014, August 13).

Introduction to basic inequalities in one variable (L7.2)

[Video]. YouTube.

Finding Domain and Range From Graphs

Mathispower4u. (2019, May 16).

Determine the domain and range from a graph: semicircle

[Video]. YouTube.

Mathispower4u. (2013, May 29).

Ex: Give the domain and range given the graph of a function

[Video]. YouTube.

Finding the Domains and Ranges of the Toolkit Functions

Mathispower4u. (2014, August 13).

Introduction to basic inequalities in one variable (L7.2)

[Video]. YouTube.

Graphing Piecewise-Defined Functions

Piecewise Functions

Khan Academy. (2015, March 5).

Piecewise function formula from graph | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Mathispower4u. (2016, July 8).

Determine a basic piecewise defined function

[Video]. YouTube.

Khan Academy. (2015, March 5).

Graphing piecewise function | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

SECTION 3.3—RATES OF CHANGE AND BEHAVIOR OF GRAPHS

Finding Average Rate of Change of a Function

Mathispower4u. (2012, June 14).

Ex: Find the average rate of change from a table – Temperatures

[Video]. YouTube.

Mathispower4u. (2012, June 14).

Ex: Find the average rate of change given a function rule

[Video]. YouTube.

Mathispower4u. (2012, June 14).

Ex: Find the average rate of change from a graph

[Video]. YouTube.

Using a Graph to Determine Where a Function is Increasing, Decreasing, or Constant

Mathispower4u. (2013, June 25).

Ex: Determine if a function is incr, decr, or constant from graph, table, and ordered pairs

[Video]. YouTube.

Mathispower4u. (2012, June 15).

Ex: Increasing / decreasing / relative extrema from analyzing a graph

[Video]. YouTube.

Mathispower4u. (2012, June 15).

Ex: Increasing / decreasing / relative extrema from analyzing a graph

[Video]. YouTube.

Analyzing the Toolkit Functions for Increasing or Decreasing Intervals

Fiorentino Siciliano. (2020, September 2).

Math 10 3.3. Analyzing the toolkit functions for increasing or decreasing intervals

[Video]. YouTube.

Using a Graph to Locate the Absolute Maximum and Absolute Minimum

Khan Academy. (2014, January 20).

Introduction to minimum and maximum points | Functions | Algebra I | Khan Academy

[Video]. YouTube.

Khan Academy. (2018, January 4).

How to recognize relative and absolute maxima and minima | Functions | Algebra I | Khan Academy

[Video]. YouTube.

SECTION 3.4—COMPOSITION OF FUNCTIONS

Combining Functions Using Algebraic Operations

Khan Academy. (2011, November 7).

Sum of functions | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, November 7).

Sum of functions | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, November 7).

Product of functions | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Khan Academy. (2011, November 7).

Quotient of functions | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Create a Function by Composition of Functions

Khan Academy. (2014, March 28).

Introduction to function composition | Functions and their graphs | Algebra II | Khan Academy

[Video]. YouTube.

Evaluating Composite Functions

Evaluating Composite Functions Using Tables

Khan Academy. (2016, February 12).

Evaluating composite functions: using tables | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Evaluating Composite Functions Using Graphs

Khan Academy. (2016, February 12).

Evaluating composite functions: using graphs | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Evaluating Composite Functions Using Formulas

Khan Academy. (2016, March 4).

Evaluating composite functions | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Mathispower4u. (2011, December 19).

Ex 1: Composite Function Values

[Video]. YouTube.

Mathispower4u. (2012, June 11).

Ex: Find and Evaluate a Composition of Three Functions

[Video]. YouTube.

Mathispower4u. (2014, June 25).

Ex: Evaluate Functions and Composite Function in Context of a Story (Graphing Calculator)

[Video]. YouTube.

Finding the Domain of Composite Function

Mathispower4u. (2021, September 11).

Composition of Two Function and the Domain

[Video]. YouTube.

Mathispower4u. (2021, September 11).

Composition of Three Function and the Domain

[Video]. YouTube.

Mathispower4u. (2011, December 19).

Ex 3: Domain of a Composite Function

[Video]. YouTube.

Mathispower4u. (2011, December 19).

Ex 4: Domain of a Composite Function

[Video]. YouTube.

Decomposing a Composite Function into Its Component Functions

Mathispower4u. (2012, June 11).

Ex: Decompose Functions

[Video]. YouTube.

resources_22sep/3.5, 4.1 – 4.3 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 3

.5

, 4.1–4.3

SECTION 3.5

—TRANSFORMATION OF FUNCTIONS

Graphing Functions Using Horizontal and Vertical Shifts

Identifying Vertical Shifts

Khan Academy. (2019, July 23).

Shifting functions introduction | Transformations of functions | Algebra 2 | Khan Academy

[Video]. YouTube.

Mathispower4u. (2010, July 26).

Function transformations: Horizontal and vertical translations

[Video]. YouTube.

Identifying Horizontal Shifts:

Mathispower4u. (2010, July 26).

Function transformations: Horizontal and vertical translations

[Video]. YouTube.

Combining Horizontal and Vertical Shifts:

Mathispower4u. (2012, June 22).

Ex: Determine a function rule for a translation from a table of values

[Video]. YouTube.

Graphing Functions Using Reflections About the Axes:

Mathispower4u. (2013, May 15).

Ex: Reflect a point about the x-axis, y-axis, and the origin

[Video]. YouTube.

Mathispower4u. (2010, July 26).

Function transformations: Reflections across the x-axis and y-axis

[Video]. YouTube.

Determining Even and Odd Functions:

Mathispower4u. (2012, June 11).

Introduction to odd and even functions

[Video]. YouTube.

Mathispower4u. (2012, June 11).

Ex 2: Determine if a function is odd, even, or neither

[Video]. YouTube.

Mathispower4u. (2012, June 11).

Ex 2: Determine if a function is odd, even, or neither

[Video]. YouTube.

Vertical Stretches and Horizontal Compressions:

Mathispower4u. (2010, July 26).

Function transformations: Horizontal and vertical stretches and compressions

[Video]. YouTube.

Mathispower4u. (2013, May 15).

Determine a horizontal stretch or horizontal compression

[Video]. YouTube.

Mathispower4u. (2013, May 15).

Determine a vertical stretch or vertical compression

[Video]. YouTube.

Performing a Sequence of Transformations:

Mathispower4u. (2020, August 14).

Graph a transformation of a line segment: g(x)=-af(x+c)+d (Stretch)

[Video]. YouTube.

Mathispower4u. (2010, July 26).

Graphing multiple function transformations – Part 1 of 2

[Video]. YouTube.

Mathispower4u. (2010, July 26).

Graphing multiple function transformations – Part 2 of 2

[Video]. YouTube.

Mathispower4u. (2010, July 26).

Functions transformations: A summary

[Video]. YouTube.

SECTION 4.1—LINEAR FUNCTIONS

Representing a Linear Function in Word Form:

Khan Academy. (2010, June 12).

Recognizing linear functions | Linear equations and functions | 8th grade | Khan Academy

[Video]. YouTube.

Representing a Linear Function in Function Notation:

Mathispower4u. (2012, December 28).

Linear functions

[Video]. YouTube.

Representing a Linear Function in Tabular Form:

Mathispower4u. (2015, April 27).

Determine if a table of values represents a linear function (L9.5)

[Video]. YouTube.

Representing a Linear Function in Graphical Form:

Mathispower4u. (2017, July 10).

Linear Function as a table, graph, and equation (cell phone plan)

[Video]. YouTube.

Determining Whether a Linear Function is Increasing, Decreasing, or Constant:

Mathispower4u. (2012, December 28).

Ex: Determine if a linear function is increasing or decreasing

[Video]. YouTube.

Interpreting Slope as a Rate of Change:

Mathispower4u. (2009, September 15).

Rate and slope

[Video]. YouTube.

Mathispower4u. (2012, December 28).

Ex: Find the average rate of change – miles per hour

[Video]. YouTube.

Writing and Interpreting an Equation for a Linear Function:

Mathispower4u. (2015, April 23).

Interpreting a linear function in slope-intercept form (L10.5)

[Video]. YouTube.

Modeling Real-World Problems with Linear Functions:

Mathispower4u. (2015, April 23).

Interpreting a linear function in slope-intercept form (L10.5)

[Video]. YouTube.

Mathispower4u. (2015, October 15).

Ex: Determine the domain and range from the graph function modeling a submarine ascent

[Video]. YouTube.

Khan Academy. (2010, June 12).

Modeling with linear equations example 1 | Linear equations and functions | 8th grade | Khan Academy

[Video]. YouTube.

Graphing Linear Functions:

Mathispower4u. (2016, January 15).

Ex: Graph a linear function using a table of values (function notation)

[Video]. YouTube.

Mathispower4u. (2016, July 7).

Write and graph a linear function by making a table of values (intro)

[Video]. YouTube.

Graphing a Function Using y-intercept and Slope:

Mathispower4u. (2010, July 15).

Ex 1: Graph a linear equation in slope-intercept form

[Video]. YouTube.

The Organic Chemistry Tutor. (2018, October 3).

Ex 2: Graph a linear equation in slope-intercept form

[Video]. YouTube.

Graph a Function Using Transformations:

Mathispower4u. (2016, July 7).

Graph a linear function as a transformation of f(x)=x

[Video]. YouTube.

Mathispower4u. (2011, September 5).

Ex 1: Graph a linear equation in slope-intercept form

[Video]. YouTube.

SECTION 4.2—MODELING WITH LINEAR FUNCTIONS

Building Linear Models From Verbal Descriptions:

Mathispower4u. (2017, June 16).

Write basic expressions from words modeling situations

[Video]. YouTube.

Mathispower4u. (2014, November 26).

Ex: Determine a linear function from an application (school enrollment) (09x-36)

[Video]. YouTube.

Using a Given Intercept to Build a Model:

Mathispower4u. (2014, June 27).

Ex: Linear function population growth (parallel lines application)

[Video]. YouTube.

Using a Given Input and Output to Build a Model:

Mathispower4u. (2020, February 5).

Linear equation app: Modeling tuition cost using a linear equation

[Video]. YouTube.

Using a Diagram to Build a Model:

Mathispower4u. (2015, October 15).

Ex: Determine the domain and range from the graph function modeling a submarine ascent

[Video]. YouTube.

Modeling a Set of Data with Linear Functions:

Mathispower4u. (2015, October 18).

Ex: Model the cost of a rental truck using a linear function (m and b given)

[Video]. YouTube.

SECTION 4.3—FITTING LINEAR MODELS TO DATA

Drawing and Interpreting Scatter Plots:

Khan Academy. (2015, June 19).

Constructing a scatter plot | Regression | Probability and Statistics | Khan Academy

[Video]. YouTube.

Khan Academy. (2015, June 19).

People smoking less over time scatter plot | Regression | Probability and Statistics | Khan Academy

[Video]. YouTube.

Finding the Line of Best Fit:

Mathispower4u. (2012, December 17).

Ex: Graphical interpretation of a scatter plot and line of best fit

[Video]. YouTube.

Khan Academy. (2015, August 18).

Smoking in 1945 | Data and modeling | 8th grade | Khan Academy

[Video]. YouTube.

Finding the Line of Best Fit Using a Graphing Utility:

Mathispower4u. (2015, November 6).

Ex: Determine a Line of best fit on the TI84 and make predictions

[Video]. YouTube.

Mathispower4u. (2014, November 18).

Linear regression using Desmos

[Video]. YouTube.

Distinguishing Between Linear and Nonlinear Models:

Mathispower4u. (2011, March 28).

Introduction to regression analysis

[Video]. YouTube.

Fitting Regression Line to a Set of Data:

Khan Academy. (2018, April 24).

Introduction to inference about slope in linear regression | AP Statistics | Khan Academy

[Video]. YouTube.

Mathispower4u. (2012, October 11).

Basic linear regression example on the TI84

[Video]. YouTube.

Mathispower4u. (2014, November 18).

Linear regression using Desmos

[Video]. YouTube.

resources_22sep/5.1 – 5.3 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 5

.1–5

.3

SECT

ION 5.1

—QUADRATIC FUNCTIONS

Recognizing Characteristics of Parabolas

Khan Academy. (2017, April 3).

Intro to parabolas | Khan Academy

[Video] YouTube.

Mathispower4u. (2018, December 7).

Determine key components and equation from a table of a quadratic

[Video]. YouTube.

Understanding How the Graphs of Parabolas Are Related to Their Quadratic Functions

Mathispower4u. (2011, November 30).

Ex1: Graph a quadratic function in general form

[Video]. YouTube.

Mathispower4u. (2010, July 15).

Graphing quadratic functions in standard form (vertex form)

[Video]. YouTube.

Mathispower4u. (2018, December 7).

Determine key components and graph a quadratic function y=-x^2-6x-5

[Video]. YouTube.

Mathispower4u. (2012, January 9).

Ex: Find the equation of a quadratic function from a graph

[Video]. YouTube.

Finding the Domain and Range of a Quadratic Function

Khan Academy. (2011, November 7).

Domain and range of a function given a formula | Algebra II | Khan Academy

[Video]. YouTube.

Determining the Maximum and Minimum Values of a Quadratic Function

Mathispower4u. (2015, September 25).

Ex: Quadratic function app: Maximize area of a rectangle for a given cost of fencing (vertex)

[Video]. YouTube.

Mathispower4u. (2012, June 20).

Ex: Quadratic model application – Ticket price to maximize revenue

[Video]. YouTube.

Finding the x- and y-Intercepts of a Quadratic Function

Khan Academy. (2016, March 3).

Finding features of quadratic functions | Mathematics II | High School Math | Khan Academy

[Video]. YouTube.

SECTION 5.2—POWER FUNCTIONS AND POLYNOMIAL FUNCTIONS

Identifying Power Functions:

Mathispower4u. (2019, August 6).

What are power functions? | Functions and relations, types of functions

[Video]. YouTube.

Mathispower4u. (2014, August 19).

Ex: Determine if a function is a power function

[Video]. YouTube.

Identifying End Behavior of Power Functions:

Mathispower4u. (2018, December 17).

Determine the end behavior of power functions

[Video]. YouTube.

Identifying Polynomial Functions

Polynomial Functions

Khan Academy. (2017, March 31).

Polynomials intro | Mathematics II | High School Math | Khan Academy

[Video]. YouTube.

Identifying the Degree and Leading Coefficient of a Polynomial Function

Mathispower4u. (2014, July 9).

Ex: Polynomial terminology: name, coefficient, constant, degree

[Video]. YouTube.

Identifying Local Behavior of Polynomial Functions

Fiorentino Siciliano. (2020, September 27).

Math 10 5.2 identifying local behavior of polynomial functions

[Video]. YouTube.

Intercepts and Turning Points of Polynomials

Mathispower4u. (2012, June 12).

Turning points and x intercepts of a polynomial function

[Video]. YouTube.

SECTION 5.3—GRAPHS OF POLYNOMIAL FUNCTIONS

Recognizing Characteristics of Graphs of Polynomial Functions

Mathispower4u. (2020, April 29).

Analyze a graph using desmos to determine key components of a quadratic (incr / decr / extrema)

[Video]. YouTube.

Mathispower4u. (2012, June 12).

Ex: Determine the least possible degree of a polynomial from the graph

[Video]. YouTube.

Mathispower4u. (2012, June 15).

Ex: Increasing / decreasing / relative extrema from analyzing a graph

[Video]. YouTube.

Using Factoring to Find Zeros of Polynomial Functions

Mathispower4u. (2013, January 29).

Ex: Factor and Solve a Polynomial Equation

[Video]. YouTube.

Khan Academy. (2016, February 16).

Finding zeros of polynomials (1 of 2) | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Khan Academy. (2016, February 16).

Finding zeros of polynomials (2 of 2) | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Khan Academy. (2016, February 16).

Finding zeros of polynomials (example 2) | Mathematics III | High School Math | Khan Academy

[Video]. YouTube.

Identifying Zeros and Their Multiplicities

Mathispower4u. (2018, December 17).

Determine the zeros/roots and multiplicity from a graph of a polynomial

[Video]. YouTube.

Mathispower4u. (2018, December 17).

Find zeros, multiplicity, degree, and end behavior of a factored polynomial (Degree 6)

[Video]. YouTube.

Zeros of Polynomials

Mathispower4u. (2013, May 20).

Real zeros, factors, and graphs of polynomial functions

[Video]. YouTube.

Determining End Behavior

Khan Academy. (2013, December 18).

Polynomial end behavior | Polynomial and rational functions | Algebra II | Khan Academy

[Video]. YouTube.

Understanding the Relationship Between Degree and Turning Points

Fiorentino Siciliano. (2020, September 29).

Math 10 5.3 Understanding the relationship between degree and turning points

[Video]. YouTube.

Graphing Polynomial Functions

The Organic Chemistry Tutor. (2021, January 17).

How to graph polynomial functions using end behavior, multiplicity & zeros

[Video]. YouTube.

Using the Intermediate Value Theorem

Mathispower4u. (2013, June 19).

Intermediate value theorem

[Video]. YouTube.

Writing Formulas for Polynomial Functions

Mathispower4u. (2012, June 15).

Ex1: Find an equation of a degree 4 polynomial function from the graph of the function

[Video]. YouTube.

Mathispower4u. (2012, June 15).

Ex2: Find an equation of a degree 5 polynomial function from the graph of the function

[Video]. YouTube.

Using Local and Global Extrema

Fiorentino Siciliano. (2020, September 29).

Math 10 5.3 Example 11 using local extrema to solve applications

[Video]. YouTube.

resources_22sep/5.4 – 5.6 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 5.4

–5.6

SECTION 5.4

—DIVIDING POLYNOMIALS

Using Long Division to Divide Polynomials

Mathispower4u. (2009, November 5).

Polynomial division: Long division

[Video] YouTube.

Mathispower4u. (2018, December 18).

Polynomial long division: Degree 3 divided by ax+b with remainder

[Video] YouTube.

Using Synthetic Division to Divide Polynomials

Mathispower4u. (2011, October 9).

Ex 4: Divide a polynomial by a binomial using synthetic division

[Video] YouTube.

Mathispower4u. (2018, April 8).

Synthetic division: Degree 4 divided by degree 1 (missing term, neg k)

[Video] YouTube.

Using Polynomial Division to Solve Application Problems

Fiorentino Siciliano. (2020, September 30).

Math 10 5.4 Example 6 Using polynomial division in an application problem

[Video] YouTube.

SECTION 5.5—ZEROS OF POLYNOMIAL FUNCTIONS

Evaluating a Polynomial Using the Remainder Theorem

Mathispower4u. (2018, December 14).

Use the remainder theorem to determine if a binomial is a factor of a polynomial

[Video] YouTube.

Khan Academy. (2014, November 25).

Polynomial remainder theorem example | Polynomial and rational functions | Algebra II | Khan Academy

[Video] YouTube.

Khan Academy. (2014, November 25).

Polynomial remainder theorem to test factor | Algebra II | Khan Academy

[Video] YouTube.

Using the Factor Theorem to Solve a Polynomial Equation

The Organic Chemistry Tutor. (2018, February 13).

Factor theorem and synthetic division of polynomial functions

[Video] YouTube.

Using the Rational Zero Theorem to Find Rational Zeros

The Organic Chemistry Tutor. (2018, February 13).

Finding all zeros of a polynomial function using the rational zero theorem

[Video] YouTube.

Mathispower4u. (2012, April 30).

Ex 1: The zero feature of the ti84 to find rational zeros of a polynomial

[Video] YouTube.

Mathispower4u. (2012, April 30).

Ex 2: The zero feature of the ti84 to find rational zeros of a polynomial

[Video] YouTube.

Finding the Zeros of Polynomial Functions

Mathispower4u. (2012, April 20).

Ex 2: Find the zeros of a polynomial function – Real rational zeros

[Video] YouTube.

Using the Fundamental Theorem of Algebra

Khan Academy. (2014, March 26).

Fundamental theorem of algebra | Polynomial and rational functions | Algebra II | Khan Academy

[Video] YouTube.

Khan Academy. (2014, March 26).

Possible number of real roots | Polynomial and rational functions | Algebra II | Khan Academy

[Video] YouTube.

Using the Linear Factorization Theorem to Find Polynomials with Given Zeros

Mathispower4u. (2013, May 21).

Ex 1: Write a degree 3 polynomial function as a product of linear factors (2 imaginary)

[Video] YouTube.

Mathispower4u. (2013, May 21).

Ex 3: Write a degree 5 polynomial function as a product of linear factors

[Video] YouTube.

Using Descartes’ Rule of Signs

The Organic Chemistry Tutor. (2018, February 14).

Descartes rule of signs

[Video] YouTube.

Fiorentino Siciliano. (2020, October 5).

Math 10 5.5 Example 8 using Descartes’ rule of signs

[Video] YouTube.

Mario’s Math Tutoring. (2017, April 20).

How to use Descartes rule of signs example with a cubic function

[Video] YouTube.

Solving Real-World Applications

Fiorentino Siciliano. (2020, October 5).

Math 10 5.5 Example 9 solving real-world applications with polynomial equations

[Video] YouTube.

SECTION 5.6—RATIONAL FUNCTIONS

Using Arrow Notation

Fiorentino Siciliano. (2020, March 30).

Math 10 5.6 Using arrow notation/local and end behavior

[Video] YouTube.

Fiorentino Siciliano. (2020, March 30).

Math 10 5.6 Example 1: Using arrow notation

[Video] YouTube.

Khan Academy. (2016, March 11).

Graphs of rational functions: horizontal asymptote | Algebra II | High School Math | Khan Academy

[Video] YouTube.

Khan Academy. (2016, March 11).

Graphs of rational functions: horizontal asymptote | Algebra II | High School Math | Khan Academy

[Video] YouTube.

Solving Applied Problems Involving Rational Functions

Mathispower4u. (2014, July 2).

Ex: Rational function outputs and inputs application – average cost

[Video] YouTube.

Finding the Domains of Rational Functions

Mathispower4u. (2011, September 19).

Ex: Determine the domain of a rational function

[Video] YouTube.

Mathispower4u. (2011, December 9).

Ex: The domain of rational functions

[Video] YouTube.

Identifying Vertical Asymptotes of Rational Functions

The Organic Chemistry Tutor. (2017, September 9).

How to find the vertical asymptote of a function

[Video] YouTube.

Removable Discontinuities

CK-12 Foundation. (2017, June 19).

Removable discontinuities in rational functions

[Video] YouTube.

Khan Academy. (2016, March 10).

Discontinuities of rational functions | Mathematics III | High School Math | Khan Academy

[Video] YouTube.

Identifying Horizontal Asymptotes of Rational Functions

Mathispower4u. (2012, June 20).

Ex: Determine horizontal asymptotes of rational functions

[Video] YouTube.

The Organic Chemistry Tutor. (2018, January 24).

Horizontal asymptotes and slant asymptotes of rational functions

[Video] YouTube.

Intercepts of Rational Functions

Mathispower4u. (2012, June 20).

Ex: Find the intercepts and asymptotes of a rational function

[Video] YouTube.

Graphing Rational Functions

Mathispower4u. (2011, December 8).

Ex 1: Graphing rational functions

[Video] YouTube.

Mathispower4u. (2011, December 9).

Ex 6: Graphing rational functions

[Video] YouTube.

Writing Rational Functions

Mathispower4u. (2012, June 20).

Ex: Find a rational function given the vertical asymptotes and intercepts

[Video] YouTube.

Mathispower4u. (2012, June 20).

Ex 3: Find the equation of rational function from a graph

[Video] YouTube.

Mathispower4u. (2016, July 23).

Rational function application – concentration of a mixture

[Video] YouTube.

resources_22sep/6.1 – 6.4 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video R

esources: Sections 6

.1

–6

.4

SECTION 6

.1

—EXPONENTIAL FUNCTIONS

Identifying Exponential Functions

Nerdstudy. (2017, February 11).

Introduction to exponential functions

[Video] YouTube.

Mathispower4u. (2014, November 29).

Introduction to exponential functions in the form f(x)=ab^x – Part 1

[Video] YouTube.

Mathispower4u. (2014, November 29).

Introduction to exponential functions in the form f(x)=ab^x – Part 2

[Video] YouTube.

Evaluating Exponential Functions

Mathispower4u. (2018, December 26).

Evaluate exponential functions: Base 3 and 1/3

[Video] YouTube.

Defining Exponential Growth

Mathispower4u. (2019, January 21).

Write exponential equations given initial values and growth or decay rate

[Video] YouTube.

Mathispower4u. (2019, January 21).

Write an exponential equation to model world population growth

[Video] YouTube.

Finding Equations of Exponential Functions

Mathispower4u. (2012, June 26).

Ex: Find an exponential growth function given two points – Initial value given

[Video] YouTube.

Mathispower4u. (2012, June 26).

Ex: Find an exponential function given two points – Initial value not given

[Video] YouTube.

Mathispower4u. (2012, June 26).

Ex: Find the equation of a transformed exponential function from a graph

[Video] YouTube.

Applying the Compound-Interest Formula

The Organic Chemistry Tutor. (2016, December 7).

Compound interest formula explained, investment, monthly & continuously, word problems, algebra

[Video] YouTube.

Mathispower4u. (2013, October 30).

Ex: Compounded interest formula – Determine deposit needed (present value)

[Video] YouTube.

Evaluating Functions with Base e

Mathispower4u. (2018, December 26).

Evaluate exponential functions: Base e

[Video] YouTube.

Investigating Continuous Growth

Mathispower4u. (2011, December 30).

Ex: Exponential growth function – Population

[Video] YouTube.

Mathispower4u. (2012, June 26).

Exponential function application (y=ae^(kt)) – Bacteria growth

[Video] YouTube.

Mathispower4u. (2016, August 7).

Determine a continuous exponential decay function and make a prediction

[Video] YouTube.

SECTION 6.2—GRAPHS OF EXPONENTIAL FUNCTIONS

Graphing Exponential Functions

Mathispower4u. (2019, October 19).

Graphing basic exponential functions: Growth and decay

[Video] YouTube.

Mathispower4u. (2016, August 7).

Graph a basic exponential function using a table of values

[Video] YouTube.

Mathispower4u. (2011, December 21).

Ex: Determine exponential graphs that have specific characteristics – y = ab^x

[Video] YouTube.

Graphing Transformations of Exponential Functions

Mathispower4u. (2012, June 22).

Ex: Match the graphs of translated exponential function to equations

[Video] YouTube.

Mathispower4u. (2013, May 15).

Ex: Equations of a transformed exponential function

[Video] YouTube.

Mathispower4u. (2015, December 21).

Ex: Determine the equation of a transformation of y=2^x

[Video] YouTube.

Mathispower4u. (2017, January 16).

Graphing exponential functions with e, transformations, domain and range, asymptotes, precalculus

[Video] YouTube.

Mathispower4u. (2012, June 26).

Ex: Find the equation of a transformed exponential function from a graph

[Video] YouTube.

SECTION 6.3—LOGARITHMIC FUNCTIONS

Converting from Logarithmic to Exponential Form

Mathispower4u. (2012, June 18).

Ex: Write logarithmic equations as exponential equations – Variables

[Video] YouTube.

Converting from Exponential to Logarithmic Form

Mathispower4u. (2011, December 23).

Ex: Write exponential equations as logarithmic equations

[Video] YouTube.

Mathispower4u. (2012, June 18).

Ex: Write exponential equations as logarithmic equations – Variables

[Video] YouTube.

Evaluating Logarithms

Mathispower4u. (2012, June 18).

Ex 1: Evaluate logarithms without a calculator – Whole numbers

[Video] YouTube.

Using Common Logarithms

Mathispower4u. (2012, June 18).

Ex: Evaluate common logarithms without a calculator

[Video] YouTube.

Mathispower4u. (2012, June 18).

Ex: Evaluate common logarithms on a calculator

[Video] YouTube.

Using Natural Logarithms:

Mathispower4u. (2011, December 23).

Ex: Evaluate natural logarithms on the calculator

[Video] YouTube.

Khan Academy. (2011, November 8).

Natural logarithm with a calculator | Logarithms | Algebra II | Khan Academy

[Video] YouTube.

SECTION 6.4—GRAPHS OF LOGARITHMIC FUNCTIONS

Finding the Domain of a Logarithmic Function

Mathispower4u. (2018, December 28).

Determine the domain, range, and asymptote of a log function y=-ln(x-6)

[Video] YouTube.

Mathispower4u. (2018, December 28).

Determine the domain, range, and asymptote of a log function y=-log_3(x)+4

[Video] YouTube.

Graphing Logarithmic Functions

Mathispower4u. (2018, December 28).

Graphing log functions by hand: y=log_(1/2)(x)

[Video] YouTube.

Mathispower4u. (2018, December 28).

Graphing logarithmic functions using Desmos.com

[Video] YouTube.

Graphing Transformations of Logarithmic Functions

Mathispower4u. (2018, December 29).

Graphing log functions by hand: y=log_3(x)+2

[Video] YouTube.

Mathispower4u. (2019, July 31).

Graphing logarithmic functions (example 1) | Algebra 2 | Khan Academy

[Video] YouTube.

Mathispower4u. (2017, January 18).

Graphing logarithmic functions with transformations, asymptotes, and domain & range

[Video] YouTube.

resources_22sep/6.5 – 6.8 video resources_MAT-121-sep22 x

MAT-121: COLLEGE ALGEBRA

Video Resources: Sections 6.5–6.8

SECTION 6.5—LOGARITHMIC PROPERTIES

Using the Product Rule for Logarithms

Mathispower4u. (2016, August 11).

Expand logarithms using the product rule for logs

[Video] YouTube.

Mathispower4u. (2016, August 11).

Expand logarithms using properties of logarithms (expressions)

[Video] YouTube.

Using the Quotient Rule for Logarithms

Mathispower4u. (2012, June 26).

Ex: Combine a sum and difference of two logarithms

[Video] YouTube.

Mathispower4u. (2011, December 27).

Ex 2: Combine a logarithmic expression into one logarithm

[Video] YouTube.

Mathispower4u. (2016, August 12).

Combine logarithms using properties of logarithms

[Video] YouTube.

Using the Power Rule for Logarithms

Khan Academy. (2011, November 8).

Logarithm of a power | Logarithms | Algebra II | Khan Academy

[Video] YouTube.

Intuitive Math. (2020, March 21).

Log power rule proof

[Video] YouTube.

Khan Academy. (2007, November 10).

Proof: a log b = log(b^a), log a – log b = log(a/b) | Logarithms | Algebra II | Khan Academy

[Video] YouTube.

Mathispower4u. (2010, July 15).

The properties of logarithms

[Video] YouTube.

Expanding Logarithmic Expressions

Mathispower4u. (2012, June 28).

Ex: Expand a logarithm containing a radical

[Video]. YouTube.

Mathispower4u. (2016, August 11).

Expand logarithms using properties of logarithms (expressions)

[Video] YouTube.

Mathispower4u. (2011, December 27).

Ex 1: Expand logarithmic expressions

[Video] YouTube.

Condensing Logarithmic Expressions

Mathispower4u. (2016, August 12).

Combine logarithms using properties of logarithms

[Video] YouTube.

Mathispower4u. (2012, June 26).

Ex: Combine a sum and difference of two logarithms

[Video] YouTube.

Using the Change-of-Base Formula for Logarithms

Mathispower4u. (2010, July 15).

Logarithms: Change of base formula

[Video] YouTube.

Mathispower4u. (2011, December 27).

Ex: Change of base formula to evaluate logarithmic expressions

[Video] YouTube.

SECTION 6.6—EXPONENTIAL AND LOGARITHMIC EQUATIONS

Using Like Bases to Solve Exponential Equations

Mathispower4u. (2010, July 15).

Solving exponential equations – Part 1 of 2

[Video] YouTube.

Mathispower4u. (2011, December 21).

Ex 4: Solve exponential equations using like bases – No logarithms

[Video] YouTube.

Mathispower4u. (2011, December 21).

Ex 6: Solve exponential equations using like bases – No logarithms

[Video] YouTube.

Solving Exponential Equations Using Logarithms

Mathispower4u. (2010, July 15).

Solving exponential equations – Part 1 of 2

[Video] YouTube.

Mathispower4u. (2010, July 15).

Solving exponential equations – Part 2 of 2

[Video] YouTube.

Mathispower4u. (2011, December 29).

Ex 1: Solve exponential equations using logarithms

[Video] YouTube.

Using the Definition of a Logarithm to Solve Logarithmic Equations

Mathispower4u. (2012, June 26).

Ex: Solve a bas