Free Printable Unit 6 Rational Functions

1.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

2.

What is the Vertical Asymptotes?

a)

x= -4

b)

x= -4,5

c)

x= -5,5

d)

x= 4

3.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

4.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

5.

Find the horizontal asymptote.

a)

None

b)

y=-2

c)

y=2

d)

y=0

6.

What is the horizontal asymptote of the function given?

a)

y = 2

b)

x = 1

c)

x = 2

d)

y = -1

7.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

8.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

9.

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

10.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

11.

What are the asymptotes?

a)

x=-1 y = -3

b)

x=1 y = -3

c)

x=-1 y =3

d)

x=1, y=3

12.

Find the vertical asymptote(s).

a)

x = 3 and x = -7

b)

x = 3

c)

x = -7

d)

x = -4

13.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

14.

Factor and cancel out in order to simplify.

a)

9(x+10)

b)

x+10

c)

9

d)

x+9

15.

(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)

16.

Find the domain of the function. f(x) = -2 / x+3

a)

x cannot equal to 3

b)

x cannot equal to 1

c)

x cannot equal to -3

d)

All real numbers

17.

Find the domain of the function. f(x) = x /2x+4

a)

x cannot equal to 2

b)

x cannot equal to 4

c)

x cannot equal to -2

d)

All real numbers

18.

Find the domain of the function. f(x) = x³ / x+8

a)

x cannot equal to 2

b)

x cannot equal to -2

c)

x cannot equal to -8

d)

All real numbers

19.

What is the X-Intercept?

a)

(0,0)

b)

(4,0)

c)

(0,4)

d)

(-5,0)

20.

What are the x-intercepts?

a)

(2/3, 0)

b)

(4,0) and (-2,0)

c)

(-8,0) and (1,0)

d)

(-4,0) and (2,0)

21.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

22.

What is the definition of an ASYMPTOTE?

a)

A curved line.

b)

A line that only touches the origin.

c)

A line that only lives on the first quadrant.

d)

A line that a curve approaches, as it heads towards infinity.

23.

What is the name of this function?

a)

Parabola

b)

Rational Function

c)

Ellipse

d)

Cubic

24.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

25.

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

26.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

27.

Which is the graph of the rational equation:

a)

b)

c)

d)

28.

Which function matches this graph?

a)

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

b)

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

c)

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

d)

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

29.

Which function matches this graph?

a)

$f\left(x\right)=\frac{-4}{x}-2$

b)

$f\left(x\right)=\frac{-4}{x}+2$

c)

$f\left(x\right)=\frac{-4}{x-2}$

d)

$f\left(x\right)=\frac{-4}{x+2}$

30.

Which functions match this graph?

a)

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

b)

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

c)

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

d)

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

31.

Write the equation for the graph.

a)

$y=x$

b)

$y=x^2$

c)

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

d)

$y=\left|x\right|$

32.

Write the equation for the graph.

a)

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

b)

$y=x+3$

c)

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

d)

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

33.

Write the equation for the graph.

a)

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

b)

$y=\frac{1}{x+1}+2$

c)

$y=\frac{1}{x+1}-2$

d)

$y=\frac{1}{x-2}+1$

34.

Write the equation for the graph.

a)

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

b)

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

35.

What is the range of the function?

a)

$x=-1$

b)

$x\ne-1$

c)

$y=-2$

d)

$y\ne-2$

36.

What is the domain of the function?

a)

$x=-1$

b)

$x\ne-1$

c)

$y=-2$

d)

$y\ne-2$

37.

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)

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

38.

What is the domain of the function?
$y=\frac{1}{x}+3$

a)

$y\ne3$

b)

$y=3$

c)

$x=0$

d)

$x\ne0$

39.

What is the range of the function?
$y=\frac{1}{x}+3$

a)

$y\ne3$

b)

$y=3$

c)

$x=0$

d)

$x\ne0$

40.

Write the equation for the graph.

a)

$y=\frac{1}{x+2}+1$

b)

$y=\frac{1}{x+2}-1$

c)

$y=\frac{1}{x-2}+1$

d)

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

41.

Find the equation of the graph

a)

b)

c)

d)

42.

How many discontinuities does f(x) have?

a)

None

b)

1

c)

2

d)

3

43.

How many vertical asymptotes does f(x) have?

a)

None

b)

1

c)

2

d)

3

44.

Find the horizontal asymptote of f(x)

a)

None

b)

y=6

c)

y=1/3

d)

y=3

45.

Select all the functions that have a slanted asymptote?

a)

b)

c)

d)

46.

Which asymptotes are determined by looking at the denominator of a function?

a)

vertical

b)

horizontal

c)

slant

d)

none

47.

Choose the correct graph that matches with the equation.

a)

A

b)

B

c)

C

d)

D

48.

Which is the graph of the rational equation:

a)

b)

c)

d)

49.

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)

50.

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)

51.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

52.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

53.

Find the hole of the function.
x²- 9x+20
___________
4x² - 12x- 40

a)

x =5

b)

x=0

c)

x=4

d)

x=-2

54.

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

a)

vertical

b)

horizontal

c)

slant

d)

none

55.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 2

d)

x= -2

56.

Name any holes of the function.

a)

x=0

b)

none

c)

x=1

57.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

58.

Where is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

59.

Where is there a hole on the graph of the function?

a)

x = 2

b)

x = -2

c)

There are no holes.

d)

x = 5

60.

How many vertical asymptotes does the function have?

a)

None

b)

1

c)

2

d)

3

61.

Find the vertical asymptotes and holes of the function.

a)

Holes: None;

VA: x = 1, -3

b)

Holes: x = -3;

VA: x = 1

c)

Holes: x = -3, 1

VA: None

d)

Holes: x = 1

VA: x = -3

62.

State the vertical asymptote.

a)

x = -2/5

b)

x = -5/2

c)

x = -5

d)

x = 2

63.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

64.

A hole occurs when....

a)

You wear pants that are too tight.

b)

A factor from the numerator cancels with a factor in the denominator.

c)

The degree of the numerator is one more than the degree of the denominator.

d)

The denominator cannot be factored.

65.

Find the vertical asymptotes and holes of the function.

a)

Holes: None;

VA: x = 1, -3

b)

Holes: x = -3;

VA: x = 1

c)

Holes: x = -3, 1

VA: None

d)

Holes: x = 1

VA: x = -3

66.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

67.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

68.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

69.

a)

None

b)

x = 2

c)

x = 3

d)

x = 4

70.

What is the Horizontal Asymptote?

a)

None

b)

y= 0

c)

y= 1

d)

y= 5/4

71.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

72.

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

a)

vertical

b)

horizontal

c)

slant

d)

none

73.

What is/are the vertical asymptote(s)?

a)

There are no vertical asymptotes

b)

x=5

c)

x=-5

d)

x=-1/2

74.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

75.

what is the equation that best matches the graph?

a)

A

b)

B

c)

C

d)

D

76.

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

77.

What is the horizontal asymptote of the function given?

a)

y = 2

b)

x = 1

c)

x = 2

d)

y = 1

78.

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

79.

Where is the hole in this graph?

a)

x = -3

b)

x = 3

c)

x = 5

d)

None

80.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

81.

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

82.

How many discontinuities does f(x) have?

a)

None

b)

1

c)

2

d)

3

83.

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.

84.

Which of the following is determined by just looking at the denominator?

a)

vertical asymptote

b)

horizontal asymptote

c)

holes

d)

slant asymptote

85.

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

86.

What is the definition of an ASYMPTOTE?

a)

A curved line.

b)

A line that only touches the origin.

c)

A line that only lives on the first quadrant.

d)

A line that a curve approaches, as it heads towards infinity.

87.

Does this function have any vertical asymptotes? If so, what are their equations? $y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$

a)

No vertical asymptotes.

b)

One vertical asymptote: x = 4

c)

Two vertical asymptotes: x = -3 and x = -7

d)

Three vertical asymptotes: x = -3, x = 4, and x = -7

88.

Find the vertical asymptote.

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

a)

x=-5

b)

x=1/2

c)

x=-1/2

d)

x=-3

e)

x=2

89.

State the range:

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

a)

$\left(-\infty,\ \frac{1}{2\ }\right)\cup\left(\frac{1}{2}\ ,\ \infty\right)$

b)

c)

d)

e)

$\left(-\infty,\ -\frac{1}{2\ }\right)\cup\left(\frac{1}{2}\ ,\ \infty\right)$

90.

State the vertical asymptote:

g\left(x\right)=\frac{\left(x+2\right)}{\left(2x+3\right)}

a)

x=2

b)

$x=\frac{2}{3}$

c)

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

d)

x=-2

e)

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

91.

What is the x-value of the hole? $g\left(x\right)=\frac{\left(x-2\right)\left(x+6\right)}{\left(x+2\right)\left(x-2\right)}$

a)

2

b)

-2

c)

-6

d)

6

92.

$f\left(x\right)=\frac{\left(x+7\right)\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(x-5\right)}$

Select all of the true statements.

a)

A hole occurs where x=3

b)

vertical asymptote at x=3

c)

vertical asymptote at x=5

d)

A hole occurs where x=5

93.

The equation of a vertical asymptote is written in the form:

a)

x=

b)

y=

c)

none of the above

94.

$h\left(x\right)=\frac{x\left(x-3\right)\left(x-6\right)\left(x+3\right)}{3x\left(x+3\right)\left(x-6\right)\left(x+7\right)}$

Identify the x-value of the hole(s).

a)

x=0

b)

x=-3

c)

x=6

d)

x=-7

e)

x=3

95.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

96.

What is the hole?

a)

( 4 , 9/8 )

b)

( -5, 0)

c)

( 5 , 10/9 )

d)

( 5 , 0 )

97.

Where are the discontinuities?

a)

holes: x=-3

asymptotes: x=-1

b)

holes: none

asymptotes: x=-1

c)

holes: x=-1

asymptotes: x=-3

d)

holes: x=-1

asymptotes: none

98.

Where are the discontinuities?

a)

holes: x=5

asymptotes: x=49

b)

holes: none

asymptotes: x=49

c)

holes: none

asymptotes: x=-7,7

d)

holes: x=5

asymptotes: x=-7,7

99.

Where are the discontinuities?

a)

holes: none

asymptotes: x=6

b)

holes: x=-3

asymptotes: x=6

c)

holes: none

asymptotes: x=-1

d)

holes: x=-3

asymptotes: x=-1

100.

Where are the discontinuities?

a)

holes: none

asymptotes: x=1/8

b)

holes: x=-1

asymptotes: x=1/8

c)

holes: none

asymptotes: x=0

d)

holes: x=-1

asymptotes: x=0

101.

Where are the discontinuities?

a)

holes: x=-1

asymptotes: x=5/3

b)

holes: x=-1

asymptotes: x=2/3

c)

holes: x=1

asymptotes: x=5/3

d)

holes: x=1

asymptotes: x=2/3

102.

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, 2)

e)

Hole at (1, -2)

103.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

104.

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

a)

b)

c)

d)

105.

The domain are the ______ values.

a)

y

b)

x

c)

Both x and y

106.

The range are the _____ values.

a)

y

b)

x

c)

Both x and y

107.

g(x), h(x), and f(x) all mean

a)

x=

b)

y=

108.

Find the domain for the function. f(x)= 2x -1 / 3x + 6

a)

x cannot equal to 2

b)

x cannot equal to -2

c)

x cannot equal to 3

d)

All real numbers

109.

Find the domain of the function. f(x) = -2 / x+3

a)

x cannot equal to 3

b)

x cannot equal to 1

c)

x cannot equal to -3

d)

All real numbers

110.

Find the domain of the function. f(x) = 3x²/ x⁴ - 1

a)

x cannot equal to 3

b)

x cannot equal to -1

c)

x cannot equal to 1

d)

All real numbers

111.

Find the domain of the function. f(x) = x³ / x+8

a)

x cannot equal to 2

b)

x cannot equal to -2

c)

x cannot equal to -8

d)

All real numbers

112.

What is the equation of the vertical asymptote?

a)

x = 0

b)

x = 4

c)

x = -1, x = 4

d)

x = -1

113.

What are the coordinates of the hole, if one exists.

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

114.

What is the equation of the slant asymptote?

a)

y = x + 1

b)

y = x + 2

c)

y = x + 3

d)

y = x

115.

What is the equation of the horizontal asymptote?

a)

y = 0

b)

y = -2

c)

y = 2

d)

There isn't one

116.

Find the x-intercept(s), if one exists.

a)

(1, 0)

b)

(-1, 0)

c)

(1, 0), (-1, 0)

d)

(0, 0), (1, 0)

117.

Graph the function.

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

a)

b)

c)

d)

118.

Graph the function.

$f\left(x\right)=\frac{-2x^2+2x+24}{x^3-x^2-12x}$

a)

b)

c)

d)

119.

Select ALL the information that applies to the given rational function.
$f\left(x\right)=\frac{x-3}{-2x^2+8x-6}$

a)

Vertical Asymptote. at x = 1

b)

No Holes

c)

Horizontal Asymptote. at y = 0

d)

y-intercept at (0, 1/2)

120.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{2x^2-2}{x^2-4x+3}$

a)

Vertical Asymptote. at x = -3 and x = 1

b)

Hole at (1, 0)

c)

Horizontal Asymptote at y = 2

d)

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

121.

Which of the following is considered as removable discontinuities?

a)

intercepts

b)

holes

c)

asymptotes

d)

domains

122.

Find the x-intercept(s), if one exists.

a)

(1, 0)

b)

(-1, 0)

c)

(1, 0), (-1, 0)

d)

(0, 0), (1, 0)

123.

Solve by cross-multiplying

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

124.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

125.

Solve by cross-multiplying.

a)

x = -1, 5

b)

No Solution

c)

x = -4, 5

d)

x= -4

126.

Identify the LCD.

a)

x²(x - 2)

b)

x(x - 2)

c)

x

d)

(x - 2)

127.

Identify the LCD.

a)

(x + 5)

b)

x²(x + 5)

c)

x

d)

x(x + 5)

128.

Solve by using the LCD.

a)

x = 4/3

b)

x = 2

c)

x = 3/4

d)

x = 2/3

129.

Solve by using the LCD.

a)

x = -2, 8

b)

x = 0, 4

c)

x = 2, -8

d)

x = 8

130.

Solve by using the LCD.

a)

x = 0, 5/2

b)

x = 5/2

c)

x = 0

d)

No Solution

131.

Solve by using the LCD.

a)

x = 1

b)

x = 2, 4

c)

x = 0, 5

d)

x = -5, -1

132.

Solve by using the LCD.

a)

x = 1

b)

x = -3

c)

x = 0

d)

x = 3

133.

Solve for x

a)

6

b)

17/5

c)

19/2

d)

- 6

134.

Solve for v

a)

- 7/6

b)

- 9/5

c)

9/5

d)

-3

135.

Solve for x

a)

5

b)

4/5

c)

1

d)

- 4

136.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

137.

Solve for x

a)

5/3, 1

b)

- 5, 1

c)

5, 2/3

d)

5, 1

138.

Solve for n

a)

- 2, - 1

b)

- 5, - 1

c)

- 2

d)

- 2, - 2/3

139.

Solve for x

a)

11

b)

5

c)

8

d)

7

140.

Solve for x

a)

A

b)

B

c)

C

d)

D

141.

Solve for c

a)

-3

b)

3

c)

4

d)

-4

142.

Solve for x

a)

a x=1/2

b)

b x=10

c)

c x=4

d)

d x=12

143.

Solve for x

a)

x = -3

b)

x = -3, 5

c)

x = 3, 5

d)

x = 5

144.

Solve for x

a)

x = 10

b)

x = -30/13

c)

x = 6

d)

no solution

145.

Solve!

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

146.

What is the least common multiple of x²-16 and x²+4x-32?

a)

(x + 4)(x – 4)(x + 8)

b)

(x-4)2 (x+8)

c)

(x + 4)(x – 4)

d)

(x - 4)(x-4)2(x + 8)

147.

a)

x = -1

b)

x = 1

c)

x = -9

d)

x = 9

148.

Solve for x.

a)

2

b)

18/5

c)

26/5

d)

6

149.

Solve the equation for x.

a)

6

b)

12

c)

0

d)

3

150.

Solve

a)

x = 0 , 4

b)

x = 1 , 3

c)

x = -4 , 0

d)

x = 5 , 2

151.

Solve!

a)

x = 5

b)

x = 4

c)

x = 5.5

d)

x = -4

152.

Solve :

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

153.

Solve the equation for x.

a)

7

b)

6

c)

14

d)

0

154.

Solve for x

a)

1/3

b)

-5.5

c)

5.5

d)

2.5

155.

a)

x = 2

b)

x = 3/4

c)

x = 4

d)

x = 1/2

156.

Solve the equation for x.

a)

6

b)

12

c)

0

d)

3

157.

Solve the equation for x.

a)

7

b)

6

c)

14

d)

0

158.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

159.

a)

x = 8.9

b)

x = 16

c)

x = 9

d)

x = 12

160.

a)

x = -1

b)

x = 1

c)

x = -9

d)

x = 9

161.

Solve!

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

162.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

163.

Solve for x

a)

x = 10

b)

x = -30/13

c)

x = 6

d)

no solution

164.

Solve for x

a)

1/3

b)

-5.5

c)

5.5

d)

2.5

165.

Solve for x

a)

4

b)

2

c)

-2

d)

-4

166.

Solve.

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

167.

Solve.

a)

x = 4.5

b)

x = -4.5

c)

x = 3

d)

x = -3

168.

a)

3/5

b)

3/4

c)

1/4

d)

4/5

169.

a)

2

b)

1

c)

-1

d)

-4

170.

A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

a)

2 hours at 105 mph
3 hours at 115 mph

b)

3 hours at 105 mph
2 hours at 115 mph

c)

1 hour at 105 mph
4 hours at 115 mph

d)

2.5 hours at 105 mph
2.5 hours at 115 mph

171.

Divide

a)

x+8/x+4

b)

x+4/x+8

c)

16/x-4

d)

x-4/x+8

172.

You have 2 machines that create boxes. Working alone, machine 1 can produce 1500 boxes in x hours. But when they work together, they can cover 1500 boxes in y hours. In terms of x and y, how many hours does it take the 2nd machine by itself to produce 1500 boxes?

a)

x/(x+y)

b)

y/(x+y)

c)

xy/(x+y)

d)

xy/(x-y)

173.

Lucy and Quinn have started a car washing business. Lucy can wash a car in 3 hours. Together, Lucy and Quinn can wash a car in 1 hour. How long does it take Quinn to wash a car by herself?

a)

It takes Quinn 4 hours.

b)

It takes Quinn 2 hours.

c)

It takes Quinn 1.5 hours.

d)

I don't know. It's too cold to wash cars! *DON'T PICK THIS!*

174.

Tim can paint the football field in 8 hours. JaQuii can paint the football field in 6 hours. Damien can paint the field in 4 hours. How long does it take them to paint the field together?

a)

It will take them 24 hours.

b)

It will take them 1.8 hours.

c)

It will take them 11 hours.

d)

It will take them 2.4 hours.

175.

Bob can mow a yard in 5 hours and Jeff can mow the same lawn in 3 hours. Which equation could be used to solve an equation to find the time it would take to mow the yard if they both mowed the lawn at the same time.

a)

$\frac{1}{3}+\frac{1}{5}+x=1$

b)

$\frac{x}{5}+\frac{1}{3}=1$

c)

$\frac{1}{5}+\frac{x}{3}=1$

d)

$\frac{x}{3}+\frac{x}{5}=1$

176.

It takes Roger 2 hours to paint a room. It takes Erin 3 hours to paint the same size of room. Which equation could be used to solve to find the time it would take to paint the room if they painted together.

a)

$\frac{1}{3}+\frac{1}{2}=6x$

b)

$\frac{x}{3}+\frac{x}{2}=6$

c)

$\frac{x}{3}+\frac{x}{2}=1$

d)

$\frac{x}{3}+\frac{x}{2}=6x$

177.

Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

a)

48 minutes

b)

50 minutes

c)

24 minutes

d)

12 minutes

178.

Catherine can paint a house in 15 hours. Dan can paint a house in 30 hours. How long will it take them working together.

a)

20 hours

b)

10 hours

c)

22 hours

d)

17 hours

179.

Igor can do a job in 20 minutes. Fred can do the same job in 30 minutes. How long will the job take if they both work together?

a)

15 minutes

b)

22 minutes

c)

25 minutes

d)

12 minutes

180.

Ned made a trip to his cabin on the lake and back. The trip there took six hours and the trip back took four hours. What was Hank's average speed on the trip there if he averaged 30 km/h on the return trip?

a)

25 km/h

b)

20 km/h

c)

16 km/h

d)

10 km/hr

181.

A passenger plane made a trip to Las Vegas and back. On the trip there it flew 432 mph and on the return trip it went 480 mph. How long did the trip there take if the return trip took nine hours?

a)

10 hours

b)

5 hours

c)

15 hours

d)

20 hours

182.

About 13 out of 20 homes have a personal computer. On a street with 60 homes, how many would you expect to have a personal computer?

a)

7 homes

b)

39 homes

c)

73 homes

d)

40 homes

183.

The waiting time to ride a roller coaster is 20 minutes when 150 people are in line. How long is the waiting time when 240 people are in line?

a)

90 min

b)

30 min

c)

32 min

d)

30 min

184.

Cookie Monster makes the perfect cookies. He uses 2 cups of chocolate chips for every 3 dozen cookies. If he makes 54 cookies, how many cups of chocolate chips does he need?

a)

3 cups

b)

16 cups

c)

32 cups

d)

48 cups

185.

Solve for x: $\frac{5}{3}-\frac{2}{x}=\frac{8}{x}$

a)

$2$

b)

$\frac{18}{5}$

c)

$\frac{26}{5}$

d)

$6$

186.

Solve: $\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$

a)

$x=-5$

b)

$x=5$

c)

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

d)

No Solution

187.

Solve for x: $\frac{1}{x}=\frac{1}{5x}-\frac{x-1}{5x}$

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

188.

State the domain restrictions.

a)

x ≠ -2

b)

x ≠ 2, 1

c)

x ≠ 2, -1

d)

x ≠ -2, 2, 1

189.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

190.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

191.

Solve and check for extraneous solutions

a)

x= - 3 &x= -8

b)

x= -3 & -8 is extraneous

c)

No Solution

d)

x= -8 & -3 is extraneous

192.

a)

A

b)

B

c)

C

d)

D

193.

To solve

\frac{x+12}{𝑥+2}≤2

, first, we transform the given inequality into its general form which is...

a)

$\frac{x+12}{𝑥+2}+2≤0$

b)

$\frac{x+12}{𝑥+2}-2≤0$

c)

$2\left(\frac{x+12}{𝑥+2}\right)≤0$

d)

$\frac{1}{2}\left(\frac{x+12}{𝑥+2}\right)≤0$

194.

Based from

\frac{-x+8}{𝑥+2}≤0

, what are the critical values of the given rational inequality?

a)

$8\ \&\ 2$

b)

$-8\ \&\ -2$

c)

$-8\ \&\ 2$

d)

$8\ \&\ -2$

195.

Solve

a)

A

b)

B

c)

C

d)

D

196.

Solve

a)

No Solution

b)

x = 6

c)

x = 7

d)

x = 5

197.

Simplify:

$\frac{3x}{10x^2}+\frac{7}{5x^2}$

a)

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

b)

$\frac{3x+7}{10x^2}$

c)

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

d)

$\frac{3x+14}{10x^2}$

198.

Simplify:

$\frac{5}{x}-\frac{3x}{6x^2}$

a)

$\frac{-33x^2}{x\left(6x^2\right)}$

b)

$\frac{30-3x}{6x}$

c)

$\frac{30x-3x}{6x-6x^2}$

d)

$\frac{27x}{6x^2}$

199.

Simplify:

$\frac{3}{x-1}+\frac{5}{6x}$

a)

$\frac{23x-5}{6x\left(x-1\right)}$

b)

$\frac{13x-5}{6x\left(x-1\right)}$

c)

$\frac{13x-5}{6x^2}$

d)

$17x-6$

200.

Simplify:

$\frac{2x}{5x}-\frac{3}{x+7}$

a)

$\frac{2x^2-x}{5x\left(x+7\right)}$

b)

$\frac{7x-21}{5x\left(x+7\right)}$

c)

$\frac{2x^2+29x}{5x\left(x+7\right)}$

d)

$\frac{2x^2-14x\ }{5x\left(x+7\right)}$

201.

Simplify:

$\frac{4x}{2x+8}-\frac{12}{x}$

a)

$\frac{4x^2+24x-96}{x\left(2x+8\right)}$

b)

$\frac{4x^2-24x+96}{x\left(2x+8\right)}$

c)

$\frac{4x^2-24x-96}{x\left(2x+8\right)}$

d)

$\frac{4x^2+24x+96}{x\left(2x+8\right)}$

202.

Simplify:

$\frac{3}{x+4}+\frac{2}{x-2}$

a)

$\frac{5x+2}{\left(x+4\right)\left(x-2\right)}$

b)

$\frac{3x-6}{\left(x-2\right)\left(x+4\right)}$

c)

$\frac{5x-10}{\left(x-2\right)\left(x+4\right)}$

d)

$\frac{6x+24}{\left(x-2\right)\left(x+4\right)}$

203.

Simplify:

$\frac{5x}{2x-3}-\frac{4x^2}{3x+1}$

a)

no solution

b)

$\frac{-8x^3+27x^2+5x}{\left(2x-3\right)\left(3x+1\right)}$

c)

$\frac{-8x^3+3x^2+5x}{\left(2x-3\right)\left(3x+1\right)}$

d)

$\frac{7x^2+17x}{\left(2x-3\right)\left(3x+1\right)}$

204.

Simplify:

$\frac{-3x}{x+5}+\frac{7}{2x-8}$

a)

$\frac{-6x^2+31x+35}{\left(x+5\right)\left(2x-8\right)}$

b)

$\frac{-6x^2-17x+35}{\left(x+5\right)\left(2x-8\right)}$

c)

$\frac{25x+35}{\left(x+5\right)\left(2x-8\right)}$

d)

$\frac{6x^2-17x+35}{\left(x+5\right)\left(2x-8\right)}$

205.

Simplify:

$\frac{8x}{x-4}-\frac{11}{3x+1}$

a)

$\frac{24x^2-3x-44}{\left(3x+1\right)\left(x-4\right)}$

b)

$\frac{24x^2+19x-44}{\left(3x+1\right)\left(x-4\right)}$

c)

$\frac{24x^2-3x+44}{\left(3x+1\right)\left(x-4\right)}$

d)

$\frac{13x^2+52x}{\left(3x+1\right)\left(x-4\right)}$

206.

Simplify:

$\frac{6x}{2}-\frac{5x}{8x}$

a)

$\frac{48x^2-5x}{2\left(8x\right)}$

b)

$\frac{24x^2-5x}{8x}$

c)

$\frac{19x}{8x}$

d)

$\frac{24x^2-10x}{8x}$

207.

Simplify:

$\frac{5}{2x}+\frac{8x}{12x}$

a)

$\frac{38x}{12x}$

b)

$\frac{8x+30}{12x}$

c)

$\frac{25+8x}{12x}$

d)

$\frac{76x}{24x^2}$

208.

Simplify:
$\frac{4x}{3x^2}+\frac{2}{x+5}$

a)

$\frac{10x^2+45x}{3x^2\left(x+5\right)}$

b)

$\frac{6x^2+24x}{3x^2\left(x+5\right)}$

c)

$\frac{10x^2+20x}{3x^2\left(x+5\right)}$

d)

$\frac{4x^2+26x}{3x^2\left(x+5\right)}$

209.

Simplify:

$\frac{6}{2x+3}-\frac{8}{x-1}$

a)

$\frac{-10x+18}{\left(x-1\right)\left(2x+3\right)}$

b)

$\frac{-10x-30}{\left(x-1\right)\left(2x+3\right)}$

c)

$\frac{22x+18}{\left(x-1\right)\left(2x+3\right)}$

d)

$\frac{22x+30}{\left(x-1\right)\left(2x+3\right)}$

210.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

211.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

212.

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

213.

Simplify (Add & Divide)

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

a)

$\frac{7x-21}{6x^2-6x}\ ,\ x\ne0,\ 1,\ 3$

b)

A $\frac{7x-21}{6x^2-6x}\ ,\ x\ne1,\ 3$

c)

$\frac{7x^2-21x}{6x^3-6x^2}\ ,\ x\ne0\ ,\ 1,\ 3$

d)

$\frac{7x^2-21x}{6x^3-6x^2}\ ,\ x\ne1,\ 3$

214.

Subtract

$\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}$

a)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$

b)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$

c)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$

d)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$

215.

Add

$\frac{7x}{x^2-5x}+\frac{x^2}{x-5}$

a)

$\frac{x^2+7}{x-5}\ ,\ x\ne5$

b)

$\frac{x^2+7}{x-5}\ ,\ x\ne0,\ 5$

c)

$\frac{x^4-5x^3+7x^2-35x}{\left(x^2-5x\right)\left(x-5\right)}\ ,\ x\ne5$

d)

$\frac{x^4-5x^3+7x^2-35x}{\left(x^2-5x\right)\left(x-5\right)}\ ,\ x\ne0,\ 5$

216.

Add

$\frac{2}{x^2-x-20}+\frac{3}{x^2+7x+12}$

a)

$\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-5,\ 3,\ 4$

b)

$\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-4,\ -3,\ 5$

c)

$\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-5,\ 3,\ 4$

d)

$\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-4,\ -3,\ 5$

217.

Add

$\frac{2x}{x^2-36}+\frac{x+4}{x+6}$

a)

$\frac{x^2-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

b)

$\frac{x^3+6x^2-24x}{\left(x^2-36\right)\left(x+6\right)}\ x\ne-6,\ 36$

c)

$\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

d)

$\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

218.

Add

$\frac{3x-2}{x+2}+\frac{2x}{4x-1}$

a)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ \frac{1}{4}$

b)

$\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ 1$

c)

$\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ \frac{1}{4}$

d)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-\frac{1}{4},\ 2$

219.

Subtract

$\frac{x^2-3}{2x+7}-\frac{2x-5}{2x+7}$

a)

$\frac{x^2-2x-8}{2x+7}\ ,\ x\ne-\frac{7}{2}$

b)

$x^2-2x-8\ ,\ x\ne0$

c)

$x^2-2x+2\ ,\ x\ne0$

d)

$\frac{x^2-2x+2}{2x+7}\ ,\ \ x\ne-\frac{7}{2}$

220.

Add

$\frac{2x-3}{4x-7}+\frac{2x-3}{4x-7}$

a)

$\frac{4x-6}{4x-7}\ ,\ x\ne-\frac{7}{4}$

b)

$\frac{4x^2-6x+9}{4x-7}\ ,\ \ x\ne\frac{7}{4}$

c)

$\frac{4x-6}{4x-7\ }\ ,\ x\ne\frac{7}{4}$

d)

An $\frac{4x-6}{8x-14},\ x\ne\frac{14}{8}$ swer 4

Unit 6 Rational Functions

Total questions: 220

Worksheet time: 14hrs 1mins

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