Name ______________________
Period ______
Due Date _____________
Homework 5.3 - Dilations
1. Identify the parent function for each graph below and then identify the transformation in each case. Write
the equation that describes the graph of the new function. Hint: try to see what happens to the coordinates
of the parent function that are easy to compare. If possible, use Desmos to check your answer.
Parent function: 𝑓 𝑥 =_____
Parent function: 𝑓 𝑥 =_____
New function: ___________
New function: ___________
2. Write an equation for a transformation that vertically shrinks the quadratic function by a factor
of 1/3 and translates it 6 units to the left.
3. Write an equation for a transformation that vertically stretches the Square Root function by a factor of 4
and then translates it 7 units down.
4. Write an equation for a transformation that vertically stretches the Absolute Value function by a factor of
15, reflects it over the x-axis and translates it 5 units to the right.
5. Identify the parent function. Then, describe how the parent function was transformed.
a. 𝑦 = −|𝑥| – 4
__________________________________________________________
b. 𝑦 = −4(𝑥 + 2)! ________________________________________________________
c. 𝑦 = −0.75 𝑥 + 3 _____________________________________________________
d. 𝑦 = 7 𝑥 + 5
!
_____________________________________________________
6. Suppose you started with the parent function f(x) = x. Answer the following questions.
a. Which parent function is this? ________________________
b. How would a vertical stretch by a factor of 4 change the function?
c. How would a vertical shrinking by a factor of 0.6 change the function?
d. What do we normally call this difference between the parent function and the answers
in (a) and (b)?
7. Challenge: Suppose you have some complicated function called f(x).
a) Try to explain how the function h(x) below differs from f(x). Use what you know about transformations
to give your best response:
ℎ 𝑥 = −3𝑓 𝑥 + 6
b) Find ℎ 7 𝑔𝑖𝑣𝑒𝑛 𝑡ℎ𝑎𝑡 𝑓 13 = 15.