wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Graphing Cubic and Cube Root Transformations

Total questions: 20

Worksheet time: 20mins

Name
Class
Date
1.

If f(x) = ∛(x) is reflected over the x-axis, vertically shrunk by a factor of 1/4, and shifted left 9, which equation is correct?

a)

1/4 ∛(x + 9)

b)

1/4 ∛(x - 9)

c)

- 1/4 ∛(x + 9)

d)

- 1/4 ∛(x - 9)

2.

Which of the facts is not true about the graph shown?

a)

The range is all real numbers.

b)

The function has been shifted 6 units right.

c)

The function has been shifted up 1 unit

d)

The function has been vertically stretched by a factor of 2.

3.

What transformations have occurred to get from the parent function f(x) to the transformed function g(x)?

a)

reflection over the x-axis,vertical shrink by a factor of -5

b)

reflection over the x-axis,vertical shrink by a factor of 1/5

c)

reflection over the x-axis,vertical stretch by a factor of 5

d)

reflection over the y-axis,vertical stretch by a factor of 5

4.

The graph of y=x3y=x^3  is graphed in blue.  Which of the following equations could be equation of the function graphed in red?

a)

y=120(x2)3+1y=\frac{1}{20}\left(x-2\right)^3+1  

b)

y=120(x+2)3+1y=\frac{1}{20}\left(x+2\right)^3+1  

c)

y=20(x2)3+1y=20\left(x-2\right)^3+1  

d)

y=20(x+2)3+1y=20\left(x+2\right)^3+1  

5.

Which of the following is the graph of y = (x – 1)3 – 7?

a)
b)
c)
d)
6.

What kind of fruits are best for a healthy diet?

a)

Apples

b)

Bananas

c)

Oranges

d)

Berries

7.
a)
A
b)
B
c)
C
d)
D
8.

If f(x) = ∛(x) is reflected over the x-axis, vertically compressed by a factor of 1/4, and shifted left 9, which equation is correct?

a)

1/4 ∛(x + 9)

b)

1/4 ∛(x - 9)

c)

- 1/4 ∛(x + 9)

d)

- 1/4 ∛(x - 9)

9.
a)

The range is y ≥ 1

b)

It has been reflected over the y-axis

c)

The function has been shifted up 1 unit

d)

The function has been shifted up 2 units

e)

Shifted to the left 6

10.

What transformations has the function undergone?

a)

reflect over y, vertical compress by 2, right 5, up 1

b)

reflect over x, horizontal compression by 2, left 5, up 1

c)

reflect over x, vertical stretch by 2, right 5, up 1

d)

reflect over y, horizontal stretch by -2, right 5, up 1

11.

Identify the function that corresponds with the graph.

a)

f(x)=x+235f\left(x\right)=\sqrt[3]{x+2}-5

b)

f(x)=x53+2f\left(x\right)=\sqrt[3]{x-5}+2

c)

f(x) = x+53+2f\left(x\right)\ =\ \sqrt[3]{x+5}+2

12.

The graph of a function is shown.  What are the domain and range of this function?

a)

Domain: (-∞, ∞)
Range: (-∞, 2]

b)

Domain: [2, ∞)
Range: (-∞, ∞)

c)

Domain: (-∞, ∞)
Range: (-∞, ∞)

d)

Domain: (-∞, 2]
Range: [2, ∞)

13.

If f(x) = x3 is changed to f(x) = - (x + 3)3 + 2, how is the graph transformed?

a)

3 units right, 2 units up, reflected across the y-axis

b)

3 units right, 2 units up, reflected across the x-axis

c)

3 units left, 2 units up, reflected across the y-axis

d)

3 units left, 2 units up, reflected across the x-axis

14.

What is the equation of this function?

a)

f(x) = (x + 2)3

b)

f(x) = (x - 2)3

c)

f(x) = ∛(x + 2)

d)

f(x) = ∛(x - 2)

15.
Describe the transformation of the graph  y = -2(x + 5)3 
a)
Shrink by 2, Reflected over y-axis, Right 5
b)
Stretch by 2, Reflected over x-axis, Left 5
c)
Stretch by 2, Reflected over x-axis, Right 5
d)
Shrink by 2, reflected over y-axis, Left 5
16.

If a cubic function is shifted left what happens to the domain?

a)

(−∞,∞)

b)

−2<x<∞

c)

(−2,0]

d)

All Cube Root Functions are different.

e)

Undefined

17.

What is the factored form for the following cubic function?

a)

x(x - 3)(x - 4)

b)

x(x + 3)(x + 4)

c)

x(x - 3)(x + 4)

d)

(x + 3)(x - 3)(x - 4)

18.

What transformations have occurred to get the graph of g(x) from the graph of f(x)?

a)

vertical shrink by a factor of 1/4,translation down 2 units

b)

vertical shrink by a factor of 1/4,translation right 2 units

c)

vertical stretch by a factor of 1/4,translation down 2 units

d)

vertical stretch by a factor of 1/4,translation right 2 units

19.

What transformations have occurred to get the graph of g(x) from the graph of f(x)?

a)

reflection over the x-axis,vertical compress by a factor of 5

b)

reflection over the y-axis,vertical compress by a factor of 5

c)

reflection over the x-axis,vertical stretch by a factor of 5

d)

reflection over the y-axis,vertical stretch by a factor of 5

20.

Identify the Transformations. 

a)

Vertical stretch by 2 and down 4

b)

Horizontal compression by ½ and down 4

c)

Vertical stretch by 2 and up 4

d)

Horizontal compression by ½ and right 4