Unit 3.2 - Function Transformations

​Unit 3.2 - Transformations of Functions

SY 2025-2026

Graphing

Graph the Parent Function:

$$f\left(x\right)=x$$

Graphing

Graph the Parent Function:

$$f\left(x\right)=x^2$$

Graphing

Graph the "Parent" Function:

$$f\left(x\right)=2^x$$

Multiple Choice

1.) Describe the transformation that occurred

p(x) = f(x + 3)

• Right 3 units

• Vertical Stretch

• Up 3 units

• Left 3 units

Multiple Choice

2.) Describe the transformation that occurred.

h(x) = f(x) + 2

• up 2 units

• left 2 units

• Vertical Strech

• right 2 units

Multiple Choice

3.) Describe the transformation that occurred.

w(x) = f(x - 7)

• Down 7

• Up 7

• Right 7

• vertical compression

Multiple Choice

4.) What are the transformations?
y=(x-2)³+4

• Horizontal shift right 2,      Vertical shift up 4

• Horizontal shift left 2 ,  Vertical shift up 4

• Horizontal shift right 2, Vertical shift down 4

• Horizontal shift left 2, Vertical shift up 4

Multiple Choice

5.) Write a function g whose graph represents the indicated transformation of the graph of f.

f(x) = x + 4; horizontal translation 3 units left

• g(x) = x + 7
• g(x) = x + 3
• g(x) = x - 4
• g(x) = x + 1

Multiple Choice

6.) Write a function g whose graph represents the indicated transformation of the graph of f.

f(x) = |2x − 5| + 3; vertical translation 2 units up

• g(x) = |2x − 5| + 1
• g(x) = |2x − 5| + 5
• g(x) = |2x + 5| + 5
• g(x) = |2x − 5| + 3

Multiple Choice

7.) What type of transformation is y =1/2 f(x)?

• Vertical Stretch

• Vertical Compression

• Horizontal Stretch

• Horizontal Compression

Multiple Choice

8.) What type of transformation is y = 2f(x)?

• Vertical Stretch

• Vertical Compression

• Horizontal Stretch

• Horizontal Compression

Multiple Choice

9.) What type of transformation is y = f(1/2 x)?

• Vertical Stretch

• Vertical Compression

• Horizontal Stretch

• Horizontal Compression

Multiple Choice

10.) What type of transformation is y =f(2x)?

• Vertical Stretch

• Vertical Compression

• Horizontal Stretch

• Horizontal Compression

Drag and Drop

11.) The function f(3x) has a ​

Placeholder

​ ​

Placeholder

by a factor of​

Placeholder

.

Drag these tiles and drop them in the correct blank above

Horizontal

Shrink

1/3

Vertical

Stretch

3

Drag and Drop

12.) The function 4f(x) has a ​

Placeholder

​ ​ ​

Placeholder

by a factor of​

Placeholder

.

Drag these tiles and drop them in the correct blank above

Vertical

Stretch

4

1/4

Horizontal

Shrink

Drag and Drop

13.) The function f(0.25x) has a ​

Placeholder

​ ​ ​

Placeholder

by a factor of​

Placeholder

.

Drag these tiles and drop them in the correct blank above

Horizontal

Stretch

4

0.25

Shrink

Vertical

Drag and Drop

14.) The function 3/2f(x) has a ​

Placeholder

​ ​ ​

Placeholder

by a factor of​​

Placeholder

.

Drag these tiles and drop them in the correct blank above

Vertical

Stretch

3/2

Shrink

Horizontal

2/3

Multiple Choice

Which solid function below is a REFLECTION of the the dotted function?

Multiple Choice

15.) The green line represents the function

$$y\ =\ x^2$$
What function is represented by the blue line?

• $$y\ =\ -x^2\ -\ 3$$  

• $$y\ =\ -x^2\ +\ 3$$  

• $$y\ =\ -\left(x+3\right)^2$$  

• $$y\ =\ -\left(x-3\right)^2$$  

Multiple Choice

16.) Function g(x) is reflected with the following transformation:

g(-x)

Does the graph reflect across the x or y axis?

• x-axis

• y-axis

Multiple Choice

17.) Function h(x) transforms f(x) with the following transformation:

h(x) = -f(x)

Does the graph reflect across the x or y axis?

• x-axis

• y-axis

Multiple Choice

18.) The dotted line is f(x). The solid line is g(x). Fill in the blank:

g(x) = _____

• -f(x)

• f(-x)

• f(x - 3)

• f(x + 3)