Unit Review: Transformations of Functions
1. Given the function f ( x) x 9 2 determine the following:
a) f (0) f ( 5) b) 𝑥, if f ( x ) 4 c) 𝑓 −1
d) Domain e) Range
2. Given ℎ(𝑥) = {(−3, 0), (−2, 1), (0, −4), (1, 1)}:
a) Is ℎ a function? b) The domain of ℎ c) The range of ℎ
d) ℎ−1 e) Is ℎ−1 a function?
3. Given 𝑓(𝑥) = 𝑥 2 + 5𝑥, write and simplify an expression for:
a) – 𝑓 (𝑥) b) 𝑓 (– 𝑥) c) – 𝑓 (– 𝑥)
4. Write the equation of the transformed function 𝑦 = 𝑥 2 that is reflected in the x-axis, vertically compressed by a factor
1
of 2, horizontally translated 3 units right, and vertically translated 6 units down.
1
5. List the transformations that have been applied to the graph of 𝑦 = 𝑓(𝑥) given 𝑦 = − 3 𝑓(2𝑥) + 4
1. Given the function f ( x) x 9 2 determine the following:
a) f (0) f ( 5) b) 𝑥, if f ( x ) 4 c) 𝑓 −1
d) Domain e) Range
2. Given ℎ(𝑥) = {(−3, 0), (−2, 1), (0, −4), (1, 1)}:
a) Is ℎ a function? b) The domain of ℎ c) The range of ℎ
d) ℎ−1 e) Is ℎ−1 a function?
3. Given 𝑓(𝑥) = 𝑥 2 + 5𝑥, write and simplify an expression for:
a) – 𝑓 (𝑥) b) 𝑓 (– 𝑥) c) – 𝑓 (– 𝑥)
4. Write the equation of the transformed function 𝑦 = 𝑥 2 that is reflected in the x-axis, vertically compressed by a factor
1
of 2, horizontally translated 3 units right, and vertically translated 6 units down.
1
5. List the transformations that have been applied to the graph of 𝑦 = 𝑓(𝑥) given 𝑦 = − 3 𝑓(2𝑥) + 4
