Free Printable Rational Functions and Their Properties

1.

The graph of a rational function can best be descirbed as

a)

A line

b)

A parabola

c)

A gradual curve

d)

A hyperbola

e)

A circle

2.

The two symmetrical parts that make up a rational function's graph are referred to as

a)

Roots

b)

Indexes

c)

Branches

d)

Curves

e)

Axis of symmetry

3.

The domain and range of the parent function of rational functions is:

a)

x≥ 0 and y≥0

b)

x≤ 0 and y≤0

c)

(−∞,∞) and

(−∞,∞)

d)

All nonzero real numbers

e)

All real numbers

4.

The asymptote(s) of the parent function of rational functions is/are:

a)

x=0

b)

y=0

c)

x=1

d)

y=1

e)

x=0 and y=0

5.

A rational function in the form shown has

a)

x= h as its horizontal asymptote and y=k as its vertical asymptote

b)

x=h as its vertical asymptote and y=k as its horizontal asymptote

c)

x = -h as its horizontal asymptote and y=k as its vertical asymptote

d)

x = -h as its vertical asymptote and y=k as its horizontal asymptote

e)

Not sure what an asymptote is but I feel none of the answers listed are correct

6.

y= $\frac{5}{x}$ is what kind of transformation from the parent function of rational equations?

a)

Vertical stretch by factor of 5

b)

Vertical compress by a factor of 5

c)

Translation 5 units to the right

d)

Translation 5 units to the left

e)

Translation 5 units up

7.

Which of the following represent(s) the domain of the function shown?

a)

x $\ne$ -3

b)

x $\ne$ 3

c)

(- $\infty$ ,3) $\cup$ (3, $\infty$ )

d)

(- $\infty$ ,-3) $\cup$ (-3, $\infty$ )

e)

(- $\infty$ ,3] $\cup$ [3, $\infty$ )

8.

What are the vertical and horizontal asymptotes of the following function?

a)

horizontal asymptote is -2 and vertical asymptote is 2

b)

horizontal asymptote is 2 and vertical asymptote is -2

c)

horizontal asymptote is -6 and vertical asymptote is 2

d)

horizontal asymptote is 1/2 and vertical asymptote is -6

e)

horizontal asymptote is 2 and vertical asymptote is -1/2

9.

What are the vertical and horizontal asymptotes of the following function?

a)

vertical asymptote is 3 and horizontal asymptote is 1

b)

vertical asymptote is 1 and horizontal asymptote is 3

c)

vertical asymptote is 1 and horizontal asymptote is -3

d)

vertical asymptote is -1/3 and horizontal asymptote is 1

e)

vertical asymptote is 3 and horizontal asymptote is -1/3

10.

What is the domain and range for the following rational function?

a)

Domain: All real numbers except -1

Range: All real numbers except 2/3

b)

Domain: All real numbers except -1

Range: All real numbers except -3/2

c)

Domain: All real numbers except 2/3

Range: All real numbers except -1

d)

Domain: All real numbers except -2/3

Range: All real numbers except -1

e)

Domain: All real numbers except 4/3

Range: All real numbers except 1

11.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

12.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

13.

What are the asymptotes?

a)

x = -1 y = -3

b)

x = 1 y = -3

c)

x = -1 y = 3

d)

x = 1 y = 3

14.

a)

All Reals Except 0

b)

All Reals

c)

All Reals Except -3

d)

All Reals Except 0 and -3

15.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

slant

d)

none

16.

What is an asymptote?

a)

an imaginary line that your function never touches

b)

a part of your function

c)

a point on your graph

d)

a type of fruit

17.

Select all the information that applies to the given rational function.

a)

V.A. at x = -3 and x = 1

b)

Hole at (1, 0)

c)

H.A. at y = 2

d)

x-intercepts at (3,0) and (1, 0)

18.

What is the X-Intercept?

a)

x= 0

b)

x= 4

c)

x= 5

d)

x= -5

19.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

20.

What are the asymptotes?

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x=-2, y = 1

c)

x=2 y =-1

d)

x=1 y =2, y =-2

21.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

22.

What (if any) holes exist?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

23.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

24.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

25.

What is the domain?

a)

All real numbers

b)

All real numbers except 4

c)

All real numbers except 2

d)

All real numbers except 2 and -2

26.

Is there a hole or a vertical asymptote?

a)

A hole when x = 2

b)

A vertical asymptote at x = 2

c)

there is no hole or vertical asymptote

27.

The holes of a rational function occur when :

a)

my pencil pokes a hole in the paper I'm working on

b)

there is something left in the denominator

c)

the value of f(0)

d)

a factor in the denominator cancels with a factor in the numerator

28.

Find the horizontal asymptote.
4x-16
_______
x²-16

a)

y=2

b)

y=1

c)

y=0

d)

none

29.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 2

d)

x= -2

30.

What is the Y-Intercept?

a)

(0, 5)

b)

(0, -6)

c)

(0, 1)

d)

(0, -5/6)

31.

Identify the parent function of the graph.

a)

Rational

b)

Cubic

c)

Exponential

d)

Sine

32.

Give the name of the parent function of

y=\frac{1}{x+6}

a)

Exponential

b)

Rational

c)

Square Root

d)

Constant

33.

Which of the following could be a graph of $y=\frac{1}{x}$ ?

a)

b)

c)

d)

34.

What is the vertical asymptote equation?

a)

x = -2

b)

x = 3

c)

x = 2

d)

x = -3

35.

What is the horizontal asymptote equation?

a)

y = -2

b)

y = 3

c)

y = 2

d)

y = -3

36.

What is the domain?

a)

All Real Numbers

b)

All Real Numbers except x = 2

c)

All Real Numbers except x = 3

d)

All Real Numbers except x = -2

37.

What is the range?

a)

All Real Numbers

b)

All Real Numbers except x = 2

c)

All Real Numbers except x = 3

d)

All Real Numbers except x = -2

38.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

39.

what is the equation that best matches the graph?

a)

A

b)

B

c)

C

d)

D

40.

What is/are the vertical asymptote(s)?

a)

There are no vertical asymptotes

b)

x=5

c)

x=-5

d)

x=-1/2

41.

What is the horizontal asymptote of the function given?

a)

y = 2

b)

x = 1

c)

x = 2

d)

y = 1

42.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

43.

What is the Horizontal Asymptote?

a)

None

b)

y= 0

c)

y= 1

d)

y= 5/4

44.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

45.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

46.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

47.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

slant

d)

none

48.

Determine whether the graph of the function has a vertical asymptote or a removeable discontinuity at x = -1.

a)

Vertical Asymptote

b)

Discontinuity

c)

Hump Day

d)

Infinite

49.

How many discontinuities does f(x) have?

a)

None

b)

1

c)

2

d)

3

50.

What is/are the x-intercepts of this graph?

a)

(-2,0) and (2,0)

b)

(-2,0)

c)

(3,0)

d)

(2,0) and (3,0

51.

Where is the hole in this graph?

a)

x = -3

b)

x = 3

c)

x = 5

d)

None

52.

What creates a hole in the graph of a rational function?

a)

Crossing the x-axis

b)

An absence of dirt.

c)

Crossing a vertical asymptote.

d)

A factor that cancels out.

53.

What is the domain and range?

a)

D : All real number x ≠ -3
R: All real number y≠ 1

b)

D : All real number x ≠ 1
R: All real number y≠ -3

c)

D : All real number x ≠ 3
R: All real number y≠ 1

d)

D : All real number x ≠ -1
R: All real number y≠ 3

54.

a)

None

b)

x = 2

c)

x = 3

d)

x = 4

55.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

56.

State the vertical asymptote: f(x)=(x-2)/(x+5).

a)

x = -2/5

b)

x = -5/2

c)

x = -5

d)

x = 2

57.

State the horizontal asymptote: (2x²-5x +1)/(x²-x)

a)

y = 2

b)

y = 1

c)

y = 0

d)

There is no HA

58.

State the vertical asymptotes: f(x) = 2 / (2x²+3x - 5)

a)

x = 1 , x = -5

b)

x = 1, x = -5/2

c)

x = -1/2, x = 5

d)

x = 0 , x = -5/2

59.

Find the domain of the rational function f(x) = x / (x²-25)

a)

(- infinity, -5) , (5, infinity)

b)

(-infinity, -5), (-5, 5) , (5, infinity)

c)

(- infinity, 5) , (5, infinity)

d)

(- infinity, 25) , (25, infinity)

60.

Find the excluded value(s).

a)

3

b)

-3

c)

0

d)

-1

61.

If you factor 6x²+7x - 3 , one of the factors is

a)

(2x - 7)

b)

(2x + 3)

c)

(2x - 1)

d)

(2x + 1)

62.

Find the vertical asymptote(s).

a)

None

b)

x = 0

c)

x= 4

d)

x = -4, 4

63.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

64.

Find the hole(s).

a)

None

b)

x = -4

c)

x = 4

d)

x = 1/2

65.

Find the vertical asymptote(s), hole(s) and horizontal asymptote.

a)

V.A.: x = -1
Holes: x = 2
H.A.: None

b)

V.A.: x = 2
Holes: x = 1
H.A.: None

c)

V.A.: x = -1
Holes: x = 2
H.A.: y = 1/4

d)

V.A.: x = 2, -1
Holes: x = None
H.A.: None

66.

What is the horizontal asymptote of the function?

a)

y=0

b)

y=1/3

c)

none

67.

List the x value for the resulting hole in the graph?

a)

2

b)

2 and 3

c)

-3

d)

3

68.

A vertical asymptote is found by setting the _________= to zero and solving for x

a)

Numerator

b)

Denominator

c)

Right side

d)

Left side

69.

How do you determine the Horizontal Asymptote?

a)

replace all x-values with 0

b)

replace the y-value with 0 or make the numerator equal 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

70.

How do you know if a factor in the denominator is a hole instead of a V.A. ?

a)

It cancels out

b)

it equals 0

c)

you set the numerator equal to 0

d)

you compare the degrees

71.

When finding the H.A., if the numerator degree is greater than the denominator degree, the answer is...

a)

y = 0

b)

none

c)

y =a / b

d)

What's an H.A.?

72.

When finding the H.A., if the numerator degree is equal to the denominator degree, the answer is...

a)

y = 0

b)

none

c)

y =a / b

d)

What's an H.A.?

73.

The first thing you should do to find all the attributes for a rational function is...

a)

Factor it all out

b)

Find the V.A.

c)

Find the H.A.

d)

Find the x / y intercepts

74.

What is the equation(s) of the vertical asymptote of the given rational function, f(x)?

a)

x = -4

b)

x = -1

c)

x = 3

d)

x = -1, x = 3

75.

True or False. There is a hole in f(x).

a)

True

b)

False

76.

What is the domain of the given function, f(x)?

a)

(-∞,2) U (2,∞)

b)

(-∞,9) U (9,∞)

c)

(-∞,∞)

77.

What is the equation of the horizontal asymptote?

a)

y = 0

b)

None

c)

y = 1

78.

Find the vertical asymptote(s) of f(x).

a)

x = -5 and x = 7

b)

x = 3 and x = 4

c)

x = 3 and x = -5

d)

There are no vertical asymptotes

79.

Find the equation of the vertical asymptote(s) of f(x).

a)

x = -5

b)

x = -5 and x = -3

c)

y = 0

d)

x = -3

80.

Determine the domain of f(x).

a)

(-∞,1) U (1,∞)

b)

(-∞,-4) U (-4,∞)

c)

(-∞,-4) U (-4,4) U (4,∞)

d)

(-∞,4) U (4,∞)

81.

Use a graphing calculator, Desmos, or app to graph the function. Click the answer choices to confirm that you practiced the graph.

a)

b)

No vertical asymptotes.

c)

Horizontal asymptote at y = 2.

82.

Use a graphing calculator, Desmos, or app to graph the function. Click the answer choices to confirm that you practiced the graph.

a)

b)

Vertical asymptote at x = -9/2

c)

Horizontal asymptote at y = 5/2

83.

Use a graphing calculator, Desmos, or app to graph the function. Click the answer choices to confirm that you practiced the graph.

a)

b)

Vertical asymptote at x = 3/4

c)

Horizontal asymptote at y = -1/4

84.

Use a graphing calculator, Desmos, or app to graph the function. Click the answer choices to confirm that you practiced the graph.

a)

b)

Vertical asymptotes at x = 4 and x = 2

c)

Horizontal asymptote at y = 0

85.

Use a graphing calculator, Desmos, or app to graph the function. Click the answer choices to confirm that you practiced the graph.

a)

b)

Vertical asymptotes around x = -2 and x = 1/3

c)

Horizontal asymptote at y = 0

86.

Use a graphing calculator, Desmos, or app to graph the function. Click the answer choice to confirm that you practiced the graph.

a)

b)

Vertical asymptotes around x = -2 and x = 5

c)

Horizontal asymptote at y = 0

87.

Use a graphing calculator, Desmos, or app to graph the function. Click the answer choices to confirm that you practiced the graph.

a)

b)

Vertical asymptotes around x = 6 and x = -1

c)

Horizontal asymptote at y = 1

88.

Use a graphing calculator, Desmos, or app to graph the function. Click the answer choices to confirm that you practiced the graph.

a)

b)

Vertical asymptotes at x = 5 and x = -2

c)

Horizontal asymptote at y = -1

89.

Use a graphing calculator, Desmos, or app to graph the function. Click the answer choices to confirm that you practiced the graph.

a)

b)

Vertical asymptotes: none!

c)

Horizontal asymptote at y = 1

90.

Use a graphing calculator, Desmos, or app to graph the function. Click the answer choices to confirm that you practiced the graph.

a)

b)

Vertical asymptotes: none!

c)

Horizontal asymptote at y = -4

91.

Select all the functions that have a slanted asymptote?

a)

b)

c)

d)

92.

Select all the following statements that are true.

a)

Vertical asymptote at x=1

b)

Vertical asymptote at x=0

c)

No vertical asymptote

d)

Hole at (-1, 0)

e)

Hole at (1, -1)

93.

$y=\frac{x^2-4x+3}{2x^2-2x}$

Select ALL the following statements that are true.

a)

Vertical asymptote at x = 1

b)

Vertical asymptote at x=0

c)

Horizontal asymptote at y = 1/2

d)

Hole at (-1, 2)

e)

Hole at (1, -1)

94.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)

b)

c)

d)

95.

Choose the best equation for the graph.

a)

b)

c)

d)

96.

Write the equation for the graph.

a)

$y=x$

b)

$y=x^2$

c)

$y=\frac{1}{x}$

d)

$y=\left|x\right|$

97.

Based on your previous answers, which could be the graph of

$\frac{x^2-6x-16}{x+5}$

a)

b)

c)

d)

98.

a)

None

b)

x = 2

c)

x = 3

d)

x = 4

99.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

100.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

101.

a)

The functions domain is All Reall #s

b)

There is a vertical asymptote at y = −2

c)

There is a vertical asymptote at x = −2

d)

The function is reflected across the x-axis

102.

What are the asymptotes of this graph?

a)

$y=1,\ x=-2$

b)

$y=-2,\ x=1$

c)

$y=2,\ x=1$

d)

$y=-1,\ x=2$

103.

What is/are the vertical asymptote(s)?

a)

There are no vertical asymptotes

b)

x=5

c)

x=-5

d)

x=-1/2

104.

What are the zeros of

\frac{x^2-6x-16}{x+5}

a)

x = 8 and x = -2

b)

x = 8, x = -2 and x = -5

c)

x = -8 and x = 2

d)

x = -5

105.

(x²+11x+24)/(x²+4x-32)

a)

A.(x+7)/(x+4)

b)

B.3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

106.

What is the point of discontinuity?

a)

x = -3

b)

(-3,2)

c)

x = -5

d)

(3,8)

107.

What creates a hole in the graph of a rational function?

a)

Crossing the x-axis

b)

An absence of dirt.

c)

Crossing a vertical asymptote.

d)

A factor that cancels out.

108.

What is the VERTICAL asymptote of this function? (click on the graph to enlarge)

a)

x=1

b)

x=-3

c)

y=1

d)

y= -3

109.

What is the HORIZONTAL asymptote of this function? (click on the graph to enlarge)

a)

x=1

b)

x=-3

c)

y=1

d)

y= -3

110.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

111.

What is/are the vertical asymptote(s)?

a)

There are no vertical asymptotes

b)

x=5

c)

x=-5

d)

x=-1/2

112.

What is the horizontal asymptote of the function given?

a)

y = 2

b)

x = 1

c)

x = 2

d)

y = 1

113.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

114.

What is the Horizontal Asymptote?

a)

None

b)

y= 0

c)

y= 1

d)

y= 5/4

115.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

116.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

117.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

118.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

slant

d)

none

119.

Determine whether the graph of the function has a vertical asymptote or a removeable discontinuity at x = -1.

a)

Vertical Asymptote

b)

Discontinuity

c)

Hump Day

d)

Infinite

120.

How many discontinuities does f(x) have?

a)

None

b)

1

c)

2

d)

3

121.

What is/are the x-intercepts of this graph?

a)

(-2,0) and (2,0)

b)

(-2,0)

c)

(3,0)

d)

(2,0) and (3,0

122.

Where is the hole in this graph?

a)

x = -3

b)

x = 3

c)

x = 5

d)

None

123.

How does the graph of $g\left(x\right)=\frac{1}{x}-3$ compare to the graph of $f\left(x\right)=\frac{1}{x}$ ?

a)

It is located 3 units higher.

b)

It is located 3 units lower.

c)

It is located 3 units to the left.

d)

It is reflected over the x-axis.

124.

How does the graph of $g\left(x\right)=\frac{1}{x+4}$ compare to the graph of $f\left(x\right)=\frac{1}{x}$ ?

a)

It is located 4 units higher.

b)

It is located 4 units to the right.

c)

It is located 4 units to the left.

d)

It is 4 times taller.

125.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

Rational Functions and Their Properties

Total questions: 125

Worksheet time: 4hrs 19mins

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