Free Printable Unit 8 Test Practice: Rational Functions

1.

What is the y-intercept?

a)

(0, -1)

b)

(0, 0)

c)

(0, 4)

d)

None

2.

a)

(-1, 0)

b)

(0, 0)

c)

(4, 0)

d)

None

3.

What are the asymptotes?

a)

x=-3, y=1

b)

x=3, y =1

c)

x=-3, y =-1

d)

x=3 y=-1

4.

Find the vertical asymptote of the rational function.

$f\left(x\right)=\frac{x^2-2x-8}{3x-2}$

a)

y=2/3

b)

x=3/2

c)

x= 2/3

d)

x=1/3

e)

none

5.

Find the x-intercept(s) of the function.
$f\left(x\right)=\frac{4x-12}{x-6}$

a)

(3,0)

b)

(6,0)

c)

(0,-2)

d)

(4,0)

e)

none

6.

What is the horizontal asymptote of the function?

a)

y=0

b)

y=1/3

c)

none

7.

What is the x-value in the coordinate of the hole?

a)

2

b)

2 and 3

c)

-3

d)

3

8.

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

a)

Numerator

b)

Denominator

c)

Right side

d)

Left side

9.

How do you find the y-intercept?

a)

replace all x-values with 0

b)

replace all y-values with 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

10.

How do you find the x-intercept?

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

11.

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

12.

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

13.

When finding the horizontal asymptote, if the numerator degree is greater than the denominator degree, the answer is...

a)

y = 0

b)

none

c)

y =a / b

14.

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

15.

Solve the inverse variation equation: $y=\frac{8}{x}$ for x when y = 4

a)

1

b)

2

c)

3

d)

4

16.

Apply inverse variation to a real-life scenario: If the speed of a car is inversely proportional to the time taken to reach the destination, and a car traveling at 60 mph reaches the destination in 4 hours, how long will it take for a car traveling at 80 mph to reach the same destination?

a)

2 hours

b)

3 hours

c)

4 hours

d)

5 hours

17.

Assume y varies inversely with x. If x=7 when y=4, what is y when x=2 ?

a)

4

b)

14

c)

7

d)

28

18.

What is the constant (k) in this inverse variation?
y = 400/x

a)

x

b)

y

c)

400

d)

Not enough information given

19.

Which of the following represents indirect variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

20.

If y varies inversely as x and x=5 when y=20, then what is the constant of variation, k?

a)

121

b)

4

c)

100

d)

6

21.

When Darcy's school bus travels at 30 miles per hour, it gets from her home to school in 12 minutes. What is the speed of Darcy's bus if it makes the same trip in 18 minutes?

a)

45 mph

b)

36 mph

c)

28 mph

d)

20 mph

22.

The cost per person to rent a mountain cabin is inversely proportional (varies inversely) to the number of people who share the rent. If the cost is $36 per person when 5 people share, what is the cost per person when 8 people share?

a)

$22.50

b)

$57.60

c)

$1.11

d)

$12.50

23.

The current in an electrical conductor varies inversely as the resistance of the conductor. What is the current when the resistance is 42 ohms, if the current is 4 amperes when the resistance is 168 ohms?

a)

21 amperes

b)

17 amperes

c)

24 amperes

d)

16 amperes

24.

The cost of producing pencils varies directly with the number of pencils produced. If the cost of producing 6,000 pencils is $400, then what will be the cost of production for 10,000 pencils?

a)

$612

b)

$604

c)

$600

d)

$610

25.

The time to complete a project varies inversely with the number of employees.
If 3 people can complete the project in 7 days, how long will it take 5 people?

a)

12 days

b)

4.2 days

c)

6.2 days

d)

10 days

26.

Suppose y varies inversely with x.
If y = 150 when x = 2, find y when x = 25.

a)

300

b)

75

c)

1,875

d)

12

27.

What is the x-intercept?

a)

(0, 0)

b)

(4, 0)

c)

(5, 0)

d)

(-5, 0)

28.

What are the x-intercepts?

a)

(2/3, 0)

b)

(4, 0)

(-2, 0)

c)

(-8, 0)

(1, 0)

d)

(-4, 0)

(2, 0)

29.

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

30.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

31.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

32.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

33.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

34.

Simplify the rational function

a)

1/(x + 5)

b)

1/(x - 5)

c)

(x - 5)(x + 5)

d)

(x - 5)/[(x - 5)(x + 5)]

35.

Simplify.

a)

4x³/(x+2)

b)

4x³/(x+10)

c)

2x³/(5x+1)

d)

2x³/(x+5)

36.

Simplify

a)

(n-2)/(n+2)

b)

(n+2)/(n-2)

c)

1/(n+2)

d)

1/(n-2)

37.

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

a)

vertical

b)

horizontal

c)

end behavior

d)

none

38.

What are the asymptotes?

a)

x=-1 y = -3

b)

x=1 y = -3

c)

x=-1 y =3

d)

x=1, y=3

39.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

40.

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

41.

Match the graph to the correct rational equation below.

a)

f(x)=x²/(x²+x-12)

b)

f(x)=4x²/(x²-x-12)

c)

f(x)=(2x²-2)/2x²

d)

f(x)=x/(x²+x-12)

42.

What is the end behavior as x approaches negative infinity?

a)

y approaches negative infinity

b)

y approaches positive infinity

c)

y approaches 1

d)

y approaches 2

43.

what is the equation that best matches the graph?

a)

A

b)

B

c)

C

d)

D

44.

What is/are the vertical asymptote(s)?

a)

There are no vertical asymptotes

b)

x=5

c)

x=-5

d)

x=-1/2

45.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

46.

What is the Horizontal Asymptote?

a)

None

b)

y= 0

c)

y= 1

d)

y= 5/4

47.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

48.

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

49.

Where is the hole in this graph?

a)

(-3, 1/2)

b)

(3, 1/8)

c)

(5, 1/8)

d)

(-5, 1/2)

50.

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.

51.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

52.

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

53.

What is the equation of the rational function graphed?

a)

b)

c)

d)

54.

Simplify

a)

(n-2)/(n+2)

b)

(n+2)/(n-2)

c)

1/(n+2)

d)

1/(n-2)

55.

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

a)

vertical

b)

horizontal

c)

end behavior

d)

none

56.

Where is the hole in this graph?

a)

x = -3

b)

x = 3

c)

x = 5

d)

None

57.

$Simplify:\ \ \frac{x^2+6x-7}{x^2-49}$

a)

$\frac{x-1}{x+7}$

b)

$\frac{x+1}{x+7}$

c)

$\frac{x-1}{x-7}$

d)

$\frac{x+1}{x-7}$

58.

$Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}$

a)

$\frac{x}{x+3}$

b)

$\frac{x}{x-3}$

c)

$\frac{x+6}{x-3}$

d)

$\frac{x}{x+6}$

59.

$Simplify:\ \ \frac{x^2+7x+10}{x^2-4}$

a)

$\frac{x-5}{x+2}$

b)

$\frac{x-5}{x-2}$

c)

$\frac{x+5}{x+2}$

d)

$\frac{x+5}{x-2}$

60.

$Simplify:\ \ \frac{x^2-25}{x^2-6x+5}$

a)

$\frac{x+5}{x-1}$

b)

$\frac{x-5}{x-1}$

c)

$\frac{x+5}{x+1}$

d)

$\frac{x-5}{x+1}$

61.

$Simplify:\ \ \frac{x^2+7x+12}{x^2+4x}$

a)

$\frac{x+3}{x+4}$

b)

$\frac{x-3}{x}$

c)

$\frac{x+3}{x}$

d)

$\frac{x+3}{x^2}$

62.

$Simplify:\ \ \ \frac{x^2-4x-45}{x^2-81}$

a)

$\frac{x+5}{x-9}$

b)

$\frac{x+5}{x+9}$

c)

$\frac{x-5}{x-9}$

d)

$\frac{x-5}{x+9}$

63.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

64.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

65.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

66.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

67.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

68.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

69.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

70.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

71.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

72.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

73.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

74.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

75.

Simplify.

a)

A

b)

B

c)

C

d)

D

76.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

77.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

(x+10)(x+8)/ 6x+60

78.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

79.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

80.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

81.

Divide the rational expressions:

a)

A.

b)

B.

c)

C.

d)

D.

82.

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

83.

Simplify the expression.

a)

b)

c)

d)

84.

Simplify the expression.

a)

b)

c)

d)

85.

Simplify the expression.

a)

b)

c)

d)

86.

Simplify the expression.

a)

b)

c)

d)

87.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

88.

Solve for x

a)

1/3

b)

-5.5

c)

5.5

d)

2.5

89.

Solve for x

a)

4

b)

2

c)

-2

d)

-4

90.

Solve the equation for x.

a)

7

b)

6

c)

14

d)

0

91.

Solve.

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

92.

Solve.

a)

x = 4.5

b)

x = -4.5

c)

x = 3

d)

x = -3

93.

Solve the equation for x.

a)

6

b)

12

c)

0

d)

3

94.

Solve for x

a)

x = 10

b)

x = -30/13

c)

x = 6

d)

no solution

95.

Solve!

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

96.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

97.

a)

x = -1

b)

x = 1

c)

x = -9

d)

x = 9

98.

a)

x = 8.9

b)

x = 16

c)

x = 9

d)

x = 12

99.

a)

x = 2

b)

x = 3/4

c)

x = 4

d)

x = 1/2

100.

a)

3/5

b)

3/4

c)

1/4

d)

4/5

101.

a)

2

b)

1

c)

-1

d)

-4

102.

Solve!

(a)

103.

Solve by using the LCD.

(a)

104.

(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)

105.

Find the horizontal asymptote.

a)

None

b)

y=-2

c)

y=2

d)

y=0

106.

Find the vertical asymptote(s).

a)

x = 3 and x = -7

b)

x = 3

c)

x = -7

d)

x = -4

107.

Suppose you translate the graph of $y=\frac{3}{x}$ so that the new graph has asymptotes at x= -5 and y=14. What is the equation for the new graph?

a)

$y=\frac{3}{x-5}-14$

b)

$y=\frac{3}{x+5}+14$

c)

$y=\frac{3}{x-14}-5$

d)

$y=\frac{3}{x+14}+5$

108.

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

109.

Write the equation for the graph.

a)

$y=\frac{1}{x+3}$

b)

$y=\frac{1}{x-3}$

c)

$y=\frac{1}{x}+3$

d)

$y=\frac{1}{x}-3$

110.

What's the vertical asymptote of the function?

a)

x = 4

b)

x = 16

c)

x = 4 , x = -4

d)

No vertical asymptote

111.

Choose the best equation for the graph.

a)

b)

c)

d)

112.

Which of the following represents the graph below?

a)

b)

c)

d)

113.

Graph the function.

$f\left(x\right)=\frac{-x+1}{x-4}$

a)

b)

c)

d)

114.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

115.

What is the horizontal asymptote of the function $y=\frac{5x+2}{2x-7}$ ?

a)

y=0

b)

y=5/2

c)

y=2

d)

y=7

116.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

117.

Determine the x-intercept(s) of this graph?

a)

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

b)

(-2,0)

c)

(3,0)

d)

(2,0) and (3,0)

118.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

119.

Simplify

a)

(x-9)

b)

$\frac{1}{x-9}$

c)

(x+9)

d)

$\frac{1}{x+9}$

120.

Simplify

a)

a

b)

b

c)

c

d)

d

121.

simplify

a)

A

b)

B

c)

C

d)

D

122.

Write the given statement in a mathematical equation.

Interest (I) varies jointly as the principal (P) amount deposited, and the rate (r) and time (t) of the deposit.

a)

I = kPrt

b)

P = kIrt

c)

T = kPIt

d)

r = kPIt

123.

Simplify: $\frac{\frac{1}{k+2}}{\frac{5}{k^2-4}}$

a)

$\frac{k-2}{5}$

b)

$\frac{k+2}{5}$

c)

$\frac{5}{k-2}$

d)

$k-2$

124.

Simplify: $\frac{\frac{1}{k+3}}{\frac{7k^2}{k^2+7k+12}}$

a)

k + 3

b)

k - 10

c)

$\frac{k-5}{3}$

d)

$\frac{k+4}{7k^2}$

125.

Simplify: $\frac{\frac{x}{5}}{\frac{4}{x+6}}$

a)

$\frac{4x}{5\left(x+6\right)}$

b)

$20x\left(x+6\right)$

c)

$\frac{x\left(x+6\right)}{20}$

d)

$\frac{x+6}{20x}$

126.

Simplify: $\frac{\frac{5k^3-25k^2}{5k^2}}{\frac{k^2+2k-35}{9}}$

a)

$\frac{4k^2}{k-7}$

b)

$\frac{9}{k+7}$

c)

$\frac{9}{4}$

d)

1

127.

$\frac{\frac{x^2-x-2}{x+6}}{\frac{x^2-1}{x+6}}$

a)

$-x-3$

b)

$\frac{x^2-x-2}{x^2+1}$

c)

$\frac{x-2}{\left(x-1\right)\left(x+1\right)}$

d)

$\frac{x-2}{x-1}$

128.

What is the horizontal asymptote?

a)

y = 0

b)

y = 1

c)

y = -1/9

d)

This graph does not have a horizontal asymptote.

129.

Solve.

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

130.

Simplify

a)

1

b)

-1

c)

Can't be simplified

d)

0

131.

Solve the equation for x.

a)

7

b)

6

c)

14

d)

0

132.

Describe all transformations from the parent function $g\left(x\right)=\frac{1}{x}$ to f(x).

a)

Shift right 5 and shift up 7

b)

Shift left 7 and shift up 5

c)

Reflect over the x-axis, shift up 7

d)

Shift left 5 and shift up 7

133.

$\frac{x+\frac{3}{x^2}}{1-\frac{2}{x}}$

a)

$\frac{x^3+3}{x^2-2x}$

b)

$\frac{x\left(x+3\right)}{x-2}$

c)

$\frac{x+3}{x-2}$

d)

$\frac{x\left(x^3+3\right)}{x-2}$

134.

If z varies inversely with the square of t, and z = 5 when t = 3, find z when t = 6

a)

10

b)

0.5

c)

1.25

d)

2.5

135.

If A varies jointly with B and C, and A = 12 when B = 2 and C = 3, find A when B = 4 and C = 5.

a)

30

b)

24

c)

36

d)

40

136.

What's the vertical asymptote of the function?

a)

x = -4, x = 1

b)

x = 4, x = -1

c)

x = -4, x = -1

d)

x = 4, x = 1

137.

The horizontal asymptote equals zero when:

a)

the degree of the numerator and denominator are equal

b)

the degree of the numerator is less than the degree of the denominator

c)

the degree of the numerator is greater than the degree of the denominator

d)

the numerator equals zero

138.

Find the horizontal asymptote:

a)

y = 0

b)

y = 1

c)

None

d)

y = 3/2

139.

Identify the type of discontinuity at $x = 3$ for the function $f(x) = \frac{x^2 - 9}{x - 3}$ .

a)

Hole

b)

Vertical Asymptote

c)

Domain

d)

Range

140.

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)

141.

Which is the graph of the rational equation:

a)

b)

c)

d)

142.

Write an equation for a rational function with an x-intercept of (–1, 0), a hole at x = 3, and a VA at x = 4.

a)

y= (x-1)(x+3) / (x+4)(x+3)

b)

y= (x-4)(x-3) / (x+1)(x-3)

c)

y= (x+1)(x-3) / (x-4)(x-3)

d)

y= (x+4)(x+3) / (x+1)(x+3)

143.

Which of the following functions does NOT have a vertical asymptote?

a)

(x+3) ∕(x²-5)

b)

x ∕ (x-3)²

c)

(x²-4) ∕ (x+2)

d)

-2 ∕ x

144.

Identify the LCD.

a)

(x + 5)

b)

x²(x + 5)

c)

x

d)

x(x + 5)

145.

Solve by using the LCD.

a)

x = -2, 8

b)

x = 0, 4

c)

x = 2, -8

d)

x = 8

146.

Solve by using the LCD.

a)

x = 1

b)

x = 2, 4

c)

x = 0, 5

d)

x = -5, -1

147.

Solve by using the LCD.

a)

x = 1

b)

x = -3

c)

x = 0

d)

x = 3

148.

Solve for x

a)

a x=1/2

b)

b x=10

c)

c x=4

d)

d x=12

149.

Solve for x:
$\frac{6}{x-1}=\frac{4}{x-2}+\frac{2}{x+1}$

a)

1

b)

2

c)

-1

d)

No Solution

Unit 8 Test Practice: Rational Functions

Total questions: 149

Worksheet time: 10hrs 18mins

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