Free Printable Cubic function and graphs

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 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)

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

5.

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)

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

6.

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)

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

7.

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)

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

8.

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

a)

b)

c)

d)

9.

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

a)

b)

c)

d)

10.

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)

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

11.

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

12.

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

13.

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

a)

(-3, -1)

b)

(0, -4)

c)

(-1, -3)

d)

(0, 0)

14.

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

a)

b)

c)

d)

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.

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)

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

17.

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

a)

(−∞,∞)

b)

−∞<y<∞

c)

(−∞,0]

d)

All Cube Root Functions are different.

18.

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

a)

(−∞,∞)

b)

−∞<x<∞

c)

(−∞,0]

d)

All Cube Root Functions are different.

19.

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

a)

(−∞,∞)

b)

−∞<x<∞

c)

(−∞,0]

d)

All Cube Root Functions are different.

20.

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

a)

(−∞,∞)

b)

−∞<y<∞

c)

(−∞,0]

d)

All Cube Root Functions are different.

21.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

22.

What is/are the zero(s) of the function?

a)

x = 4, x = 1, x = -2

b)

x = -4, x = -1, x = 2

c)

y = -2

d)

(0, -4), (0, -1), (0, 2)

23.

Which of these represents a CUBIC function?

a)

b)

c)

d)

24.

A cubic function has a degree of....

a)

1

b)

2

c)

3

d)

4

25.

Which of the following statements is/are true of the function

f\left(x\right)

(shown above)? You may select more than one statement?

a)

Positive on the interval $\left(-3,\ -1\right)$

b)

Decreasing on the interval $\left(-4,\ 2\right)$

c)

Y-intercept at $\left(0,\ 2\right)$

d)

Range of $\left(-\infty,\ \infty\right)$

e)

$f\left(x\right)$ is a cubic function

26.

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, ∞)

27.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

28.

What type of function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

29.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

30.

Which parent function matches the graph?

a)

y = |x|

b)

y = ∛(x)

c)

y = x²

d)

y = a⋅b^x

31.

Name the parent function.

a)

cubic

b)

cube root

c)

exponential

d)

quadratic

32.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

33.

What is the range of this function?

a)

(- ∞,+∞)

b)

[0, +∞)

c)

[-2, +∞)

d)

[2, +∞)

34.

Does this function have a maximum or minimum?

a)

maximum

b)

minimum

35.

What type of function is this?

a)

Linear

b)

quadratic

c)

cubic

d)

square root

36.

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, ∞)

37.

Cubic functions are used to model ___________

a)

length or width of a side

b)

area of a figure

c)

volume of a figure

d)

none of the above

38.

Find the area of a rectangle with side lengths (x +4) (x -2) inches.

4 lines

39.

Sketch the graph of each function. State the number of real zeros. Approximate the relative minima and relative maxima to the nearest tenth.

a)

b)

c)

d)

40.

Sketch the graph of each function. State the number of real zeros. Approximate the relative minima and relative maxima to the nearest tenth.

a)

b)

c)

d)

41.

Factor completely.

a)

b)

c)

d)

42.

Factor completely.

a)

b)

c)

d)

43.

Factor completely.

a)

b)

c)

d)

44.

Factor completely.

a)

b)

c)

d)

45.

Factor completely.

a)

b)

c)

d)

46.

Factor each and find all roots.

a)

b)

c)

d)

47.

Factor each and find all roots.

a)

b)

c)

d)

48.

Factor each and find all roots.

a)

b)

c)

d)

Cubic function and graphs

Total questions: 48

Worksheet time: 44mins

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