Name:
Parent Functions
Transformations of the Parent Functions
Date:
Identify the name of the parent function for each of the following. Then, indicate the effects of the parameter changes
(a, b, h, and k) on the graph of the given function, compared to its parent.
Equation
1.
1
𝑦 = 2 |2 (𝑥 + 3)|
Parent Function
Reflection
over x-axis
over y-axis
not reflected
Horizontal
Stretch/Compression
Vertical
Stretch/Compression
horizontal stretch
horizontal compression
neither
vertical stretch
vertical compression
neither
Factor: ________
2.
1
𝑦 = − 2 (𝑥 − 1)2
over x-axis
over y-axis
not reflected
horizontal stretch
horizontal compression
neither
Factor: ________
3.
𝑦 = 3(2)−(𝑥+1) − 1
over x-axis
over y-axis
not reflected
horizontal stretch
horizontal compression
neither
Factor: ________
4.
−2
𝑦 = 𝑥−3 + 4
over x-axis
over y-axis
not reflected
horizontal stretch
horizontal compression
neither
Factor: ________
5.
3
𝑦 = 4 ∙ √−4𝑥 − 5
over x-axis
over y-axis
not reflected
horizontal stretch
horizontal compression
neither
Factor: ________
Factor: ________
vertical stretch
vertical compression
neither
Factor: ________
vertical stretch
vertical compression
neither
Factor: ________
vertical stretch
vertical compression
neither
Factor: ________
vertical stretch
vertical compression
neither
Factor: ________
Vertical
Translation
Horizontal
Translation
up
down
neither
left
right
neither
Units: ____
Units: _____
up
down
neither
Units:
______
up
down
neither
Units:
______
up
down
neither
Units:
______
up
down
neither
Units:
______
left
right
neither
Units: _____
left
right
neither
Units: _____
left
right
neither
Units: _____
left
right
neither
Units: _____
Given the description of a function, write an equation for it, and get the new Domain & Range
6.
8.
𝑓(𝑥) is a quadratic function that has been reflected over the xaxis, and translated 6 units to the left.
7.
𝑔(𝑥) is an absolute value function that has been horizontally
compressed by a factor of 5, and translated 2 units down.
𝑦=
𝑦=
Domain: ________________________
Range: ________________________
Domain: ________________________
Range: ________________________
ℎ(𝑥) is a square root function that has been reflected over the x2
axis, vertically compressed by a factor of 3, and translated 1 unit
up.
9.
𝑘(𝑥) is a rational function that has been reflected over the x-axis,
vertically stretched by a factor of 1.5, and translated 3 units to
the right.
𝑦=
𝑦=
Domain: ________________________
Range: ________________________
Domain: ________________________
Range: ________________________