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Classify the following functions as one of the types of functions that we have discussed
Find an equation of the quadratic below:
Find a formula for a cubic function if 𝑓(−2) = 𝑓(1) = 𝑓(3) = 0 and 𝑓(2) = 8
Section 1.1: A Review of Functions
What is a function?
A function is a rule that assigns to each value in the domain, D, exactly one value in the
range, R.
Ex 1) Let f(x) = 2x – 3. Find
a) f(–5)
b) f(2)
Ex 2) Use the vertical line test to identify graphs in which y is a function of x.
a) b) c) d)
Ex 3) Determine whether the relations are functions:
b) c)𝑎) 2𝑥 + 𝑦2 = 16 𝑦 = 𝑥2 + 1 𝑦 = 𝑐𝑜𝑠𝑥
Once we know we have a rule that is a function, we want to know what the domain and range are for the
function.
Ex 4) Let and𝑓 𝑥( ) = 𝑥+1
𝑥−2 𝑔 𝑥( ) = 𝑥 + 2
Find the domain of each function.
Ex 5) Let f(x) = 2x – 3. State the domain of the function, and find:
a) f(–5)
b) f(2)
c) f(a +1)
d) f(x + h)
Ex 6) Simplify the difference quotient for
𝑓 𝑥+ℎ( )−𝑓(𝑥)
ℎ 𝑓 𝑥( ) = 3 − 𝑥2
Piecewise Functions:
Ex 7) Graph the piecewise function 𝑓 𝑥( ){𝑥2 − 2𝑥 + 1 𝑓𝑜𝑟 𝑥 < 2 𝑥 − 1| | 𝑓𝑜𝑟 𝑥 ≥2
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