Math III Unit 1 Review

Name: _____________________________ Function Operations/Substitution

1. Let 𝑓(𝑥) = 𝑥2 − 7𝑥 + 10 2. Let 𝑓(𝑥) = 𝑥2 − 4 𝑔(𝑥) = 5𝑥 + 12 𝑔(𝑥) = 2𝑥 − 3

a) 𝑓(−2) + 𝑔(8) = a) (𝑓 − 𝑔)(3) =

b) (𝑓 − 𝑔)(𝑥) = b) (𝑓 + 𝑔)(0) =

c) (𝑓 ∙ 𝑔)(𝑥) = c) (𝑓 ∙ 𝑔)(−1) =

d) (𝑓𝑔)(−5) d)

𝑓(3)𝑔(7)

List the Domain and Range of each relation and then determine if it’s a function.

1. {(1,7), (4,9), (−5,0), (2,2), (3,0)} 2. 3.

D: _____________________

R: _____________________

Function YES or NO D: _____________________

R: _____________________ D: _____________________

Function YES or NO R: _____________________

Function YES or NO

X Y

0 8

1 4

2 8

2 8

3 -8

Transformations: Describe in words the transformation(s) that are occurring from the parent function for each function.

1. 𝑓(𝑥) = 2|𝑥 − 6| _________________________________________________________________

2. 𝑔(𝑥) = − 12 √𝑥 − 3 _________________________________________________________________

3. ℎ(𝑥) = (𝑥 + 2)2 + 6 _________________________________________________________________

Convert to Interval Notation

1. −7 ≤ 𝑥 < 8 2. All real numbers 3. 𝑥 > 10 4. All real numbers ≠ 2

Find Domain, Range, and determine if it is a Function, One-to-One Function, or Neither.

Graphing Piecewise Functi

Graphing/Evaluating Piecewise Functions

1. Evaluate and Graph the following for 𝑓(𝑥) = {−2|𝑥 + 1|, 𝑥 ≤ 1

3, 1 < 𝑥 < 36 − 2𝑥, 𝑥 ≥ 3

a) 𝑓(10)

b) 𝑓(2)

c) 𝑓(−4)

2. Evaluate and Graph the following for 𝑔(𝑥) = {−𝑥 + 2, 𝑥 < 2𝑥 − 2, 𝑥 ≥ 2

a) 𝑔(−3)

b) 𝑔(5)

Match the Piecewise Function with its graph

Inverse of Functions

a) Find the inverse of 𝑓(𝑥) = −3𝑥 + 4

Domain of 𝑓(𝑥) =

Range of 𝑓(𝑥) =

Domain of 𝑓−1(𝑥) =

Range of 𝑓−1(𝑥) =

b) Find the inverse of 𝑓(𝑥) = 𝑥2 + 5, 𝑥 ≤ 0

Domain of 𝑓(𝑥) =

Range of 𝑓(𝑥) =

Domain of 𝑓−1(𝑥) =

Range of 𝑓−1(𝑥) =

c) Find the inverse of {(1, −3), (−2,3), (5,1), (6,4)}

Domain of 𝑓(𝑥) =

Range of 𝑓(𝑥) =

Domain of 𝑓−1(𝑥) =

Range of 𝑓−1(𝑥) =

Restrict the domain of the function 𝒇(𝒙) so that the function is one-to-one and has an inverse function.

a. 𝑓(𝑥) = (𝑥 + 3)2 b. 𝑓(𝑥) = −𝑥2 + 10