Free Printable Graphing Cubic Functions

1.

Which of the following is the graph of $y=\left(x-2\right)^3-4$

a)

b)

c)

d)

2.

Which of the following is the graph of $y=\left(x+5\right)^3-1$

a)

b)

c)

d)

3.

Which of the following is the graph of $y=-\left(x-4\right)^3+2$

a)

b)

c)

d)

4.

Which of the following is the equation for the cubic function graphed above

a)

$y=\left(x+4\right)^3+3$

b)

$y=\left(x+4\right)^3-3$

c)

$y=\left(x-4\right)^3+3$

d)

$y=\left(x-4\right)^3-3$

5.

Which of the following is the equation of the cubic function graphed above

a)

$y=-\left(x-1\right)^3+4$

b)

$y=\left(x-1\right)^3+4$

c)

$y=-\left(x+1\right)^3+4$

d)

$y=\left(x+1\right)^3+4$

6.

What is the equation of the graph shown?

a)

y= (x-2)³ + 4

b)

y= (x+2)³+ 4

c)

y = - (x-2)³+ 4

d)

y= - (x+2)³ + 4

7.

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

a)

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

b)

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

c)

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

d)

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

8.

Describe the transformation of the graph y = -(x - 4)³ + 5

a)

Up 5 and Left 4

b)

Reflect x-axis, Left 4, Up 5

c)

Reflect x-axis, Right 4, Up 5

d)

Right 4 and up 5

9.

Describe the transformation of the graph y = (x)³ + 6

a)

Right 6

b)

Left 6

c)

Up 6

d)

Down 6

10.

Describe the transformation of the graph y = - ½(x + 4)³ - 1

a)

Left 4 and Down 1

b)

Reflected x-axis, Down 1, Left 4, Compression by a factor of 1/2

c)

Reflected x-axis, Down 1, Left 4, Stretch by 1/2

d)

Reflected x-axis, Up 1, Right 4, Compression by a factor of 1/2

11.

What is the Domain of ALL Cubic Functions in interval notation?

a)

(−∞,∞)

b)

−∞<x<∞

c)

(−∞,0]

d)

All Cube Root Functions are different.

12.

What is the Range of ALL Cubic Functions in interval notation?

a)

(−∞,∞)

b)

−∞<y<∞

c)

(−∞,0]

d)

All Cube Root Functions are different.

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 for the red function?

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

15.

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

16.

Where is the point of inflection for y = -(x - 4)³ + 5

a)

(-4,5)

b)

(4,5)

c)

(-4,-5)

d)

(5,4)

17.

What is the point of inflection for the cubic function?

a)

(-5,1)

b)

(-2,1)

c)

(5,1)

d)

(-2,-5)

18.

Describe the transformation of the graph y = - ½(x + 4)³ - 1

a)

(4,1)

b)

(-4,-1)

c)

(4,-1)

d)

(-1/2, -1)

19.

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

a)

Horz shift right 2 Vert shift up 4

b)

Horz shift left 2 Vert shift down 4

c)

Horz shift right 2 Vert shift down 4

d)

Horz shift left 2 Vert shift up 4

20.

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

21.

Describe the transformation of the graph
y = ½x³

a)

Vertical compression by 1/2

b)

Horizontal compression by 1/2

c)

Vertical stretch by 2

d)

Horizontal stretch by 2

22.

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

23.

The graph shows the function f(x)=x³ in blue and another function g(x) in red. Which could be the equation for g(x)?

a)

A. g(x) = -x³

b)

B. g(x) = x³ - 1

c)

C. g(x) = (x + 1)³

d)

D. g(x) = (x - 1)³

24.

What is the y-intercept of the following cubic function?

a)

(1, 0)

b)

(0, 2)

c)

(-1, 0)

d)

(2, 0)

25.

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

26.

Describe the transformation of the graph y = - ½(x + 4)³ - 1

a)

Left 4 and Down 1

b)

Reflected x-axis, Down 1, Left 4, Shrink by 1/2

c)

Reflected x-axis, Down 1, Left 4, Stretch by 1/2

d)

Reflected x-axis, Up 1, Right 4, Shrink by 1/2

27.

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, ∞)

28.

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

29.

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)

30.

What is the Domain of ALL Cube Root Functions in interval notation?

a)

(−∞,∞)

b)

−∞<x<∞

c)

(−∞,0]

d)

All Cube Root Functions are different.

31.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

32.

Describe the transformation of the graph y = (x)³ + 6

a)

Right 6

b)

Left 6

c)

Up 6

d)

Down 6

33.

What is the Range of ALL Cube Root Functions in interval notation?

a)

(−∞,∞)

b)

−∞<y<∞

c)

(−∞,0]

d)

All Cube Root Functions are different.

34.

What is the point of inflection for the following cubic function?

a)

(-3, -1)

b)

(0, -4)

c)

(-1, -3)

d)

(0, 0)

35.

Which of the following is the graph of $y=\left(x-2\right)^3-4$

a)

b)

c)

d)

36.

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

a)

$y=-5\left(x+2\right)^3-1$

b)

$y=5\left(x+2\right)^3-1$

c)

$y=-\frac{1}{5}\left(x+2\right)^3-1$

d)

$y=\frac{1}{5}\left(x+2\right)^3-1$

37.

What is the equation of the graph shown?

a)

y= (x-2)³ + 4

b)

y= (x+2)³+ 4

c)

y = - (x-2)³+ 4

d)

y= - (x+2)³ + 4

Graphing Cubic Functions

Total questions: 37

Worksheet time: 51mins

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