Function Inverses and Transformations Retest
1. What is the inverse of f(x) = 3x ?
2. What is the inverse of g(x) = x3 ?
3. What is the inverse ofℎ(𝑥)
=
𝑥+5
4
4. 𝑦 = 𝑓(𝑥) has been transformed to 𝑦 = 𝑓(𝑘𝑥).
a. What value of k would result in a horizontal stretch by a factor of 4?
b. What value of k would result in a reflection in the y-axis?
5. The parent function 𝑦 =
1
𝑥
that has been transformed in all of the following ways:
Translated 3 units up and 7 units to the left, also, reflected in the x-axis.
Write the equation of the transformed function.
6. The parent function y = |x| has been stretched horizontally by a factor of 5 and
reflected in the y-axis.
Write the equation of the transformed function.
7. Is the domain of a function the same as the domain of the inverse of a function? If
not, how is the domain of the inverse function related to the original function?