Free Printable rational test review

1.

What is the X-Intercept?

a)

x= 0

b)

x= 4

c)

x= 5

d)

x= -5

2.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

3.

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

4.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

5.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

6.

Where is the removable discontinuity?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

7.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

8.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

9.

a)

y = 0

b)

y = 1/2

c)

y = 2

d)

None

10.

Find the horizontal asymptote.

a)

None

b)

y=-2

c)

y=2

d)

y=0

11.

What is the horizontal asymptote of this function?

a)

y=2

b)

x=1/2

c)

y=1

d)

y=1/2

12.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

13.

What is the Vertical Asymptotes?

a)

x= -4

b)

x= -4,5

c)

x= -5,5

d)

x= 4

14.

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)

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

15.

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)

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

16.

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!*

17.

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.

18.

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

19.

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

20.

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

21.

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

a)

b)

c)

d)

22.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 2

d)

y = 4

23.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

24.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1/2

d)

y = 1

25.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

26.

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

a)

b)

c)

d)

27.

What are the coordinates of the y-intercept, if one exists.

a)

(0, 0)

b)

(0, 1)

c)

(0, -1)

d)

there isn't one

28.

What are the x and y intercepts?

a)

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

b)

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

c)

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

d)

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

29.

What is the equation of the rational function graphed?

a)

b)

c)

d)

30.

What is the equation of the graph?

a)

b)

c)

d)

31.

The domain are the ______ values.

a)

y

b)

x

c)

Both x and y

32.

The range are the _____ values.

a)

y

b)

x

c)

Both x and y

33.

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

a)

x=

b)

y=

34.

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

35.

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

36.

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

37.

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

38.

Find the domain of the function. Select all answers that apply. f(x) = x+5 / 3x² - 3

a)

x cannot equal to 1

b)

x cannot equal to 3

c)

x cannot equal to -1

d)

x cannot equal to -3

39.

Find the domain of the function. Select all answers that apply. f(x) = x³ / x²- 4

a)

x cannot equal to - 2

b)

x cannot equal to -1

c)

x cannot equal to 2

d)

x cannot equal to 1

40.

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

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

41.

What is the equation of the slant asymptote?

a)

y = x + 1

b)

y = x + 2

c)

y = x + 3

d)

y = x

42.

What is the equation of the slant asymptote?

a)

y = x - 4

b)

y = 4x - 4

c)

y = 4x + 16

d)

there isn't one

43.

What is the x-coordinate of the hole, if one exists?

a)

-4

b)

-3

c)

3

d)

there isn't one

44.

What type of function is graphed?

a)

bottom heavy

b)

powers equal

c)

top heavy

45.

What type of function is shown?

a)

bottom heavy

b)

top heavy

c)

powers equal

46.

What type of function is graphed?

a)

bottom heavy

b)

powers equal

c)

top heavy

47.

What is the equation of the graph?

a)

b)

c)

d)

48.

Write an equation for the graph.

a)

b)

c)

d)

49.

Which statements are true for the given rational function. Select all that apply.

a)

The horizontal asymptote is at y = 0.

b)

There is a hole at (6, ¾ ).

c)

The vertical asymptote is at x = -2.

d)

The x and y intercepts are at the origin.

e)

The domain is all real numbers except -2.

50.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

51.

Factor and cancel out in order to simplify.

a)

9(x+10)

b)

x+10

c)

9

d)

x+9

52.

Factor and cancel out in order to simplify.

15x²/5x³

a)

3x

b)

3/x

c)

x/3

d)

5/x

53.

Simplify the rational function

a)

1/(x + 5)

b)

1/(x - 5)

c)

(x - 5)(x + 5)

d)

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

54.

Simplify the rational function

a)

1/(3x)

b)

3x(x + 1)

c)

3x

d)

(x + 1)

55.

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)

56.

Solve:
4 / (x - 6) = x / 10

a)

x = 6

b)

x = -4, 10

c)

x = 10

57.

Solve:
(4 / x) + (2 / 3) = (6 / x)

a)

x = 0

b)

x = -3

c)

x = 3

58.

Solve:
(1 / (x - 3)) = (5 / (x + 9))

a)

x = 3

b)

x = 3, -9

c)

x = 6

59.

Solve the equation for x.

a)

7

b)

6

c)

14

d)

0

60.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

61.

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)

62.

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

63.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

64.

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

a)

vertical

b)

horizontal

c)

end behavior

d)

none

65.

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

66.

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)

67.

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

68.

Where is the removable discontinuity?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

69.

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.

70.

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

71.

What is the equation of the slant asymptote?

a)

y = x + 1

b)

y = x + 2

c)

y = x + 3

d)

y = x

72.

Which asymptotes are determined by looking at the coefficients of the highest power in a function?

a)

vertical

b)

horizontal

c)

slant

d)

none

73.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

74.

State the Domain and Range.

a)

{x e R | x does not equal 5} and {y e R | y does not equal 7}

b)

{x e R | x does not equal -5} and {y e R | y does not equal 7}

c)

{x e R | x does not equal 5} and {y e R | y does not equal -7}

d)

{y e R | y does not equal 5} and {y e R | y does not equal 7}

75.

a)

Range = all real #s

b)

Range = all real #s except 2

c)

Range = all real #s except -2

d)

Range = none

76.

Determine the coordinates of the hole on the graph of
f(x)= (x²-2x + 1)/(x²+2x - 3)

a)

(1, 1/3)

b)

(-1, -1/3)

c)

(1, 0)

d)

(1, -3)

77.

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)

78.

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

79.

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

a)

$\left(-\infty,0\right)U\ \left(0,\infty\right)$

b)

$\left(-\infty,0\right]U\ \left[0,\infty\right)$

c)

$\left(-\infty,3\right)U\ \left(3,\infty\right)$

d)

$\left(-\infty,3\right]U\ \left[3,\infty\right)$

80.

Define End Behavior

a)

Tells you the y-value the function approaches as it goes towards $\pm$ infinity.

b)

The ends of the graph.

81.

What is the end behavior of this rational function?

a)

As x goes to the left, y approaches 2 from below the asymptote.

As $x\rightarrow-\infty,\ y\rightarrow2^-$

b)

As x goes to the left, y approaches 2 from above the asymptote.
As

x\rightarrow-\infty,\ y\rightarrow2^+

c)

As x goes to the right, y approaches 2 from below the asymptote.
As $x\rightarrow+\infty,\ y\rightarrow2^-$

d)

As x goes to the right, y approaches 2 from above the asymptote.
As $x\rightarrow+\infty,\ y\rightarrow2^+$

82.

What is the end behavior of this rational function?

a)

As x goes to the left, y approaches 0 from below the asymptote.

As $x\rightarrow-\infty,\ y\rightarrow0^-$

b)

As x goes to the left, y approaches 0 from above the asymptote.
As

x\rightarrow-\infty,\ y\rightarrow0^+

c)

As x goes to the right, y approaches 0 from below the asymptote.
As $x\rightarrow+\infty,\ y\rightarrow0^-$

d)

As x goes to the right, y approaches 0 from above the asymptote.
As $x\rightarrow+\infty,\ y\rightarrow0^+$

83.

What is the end behavior of this rational function?

a)

As x goes to the left, y approaches the asymptote y = x

As $x\rightarrow-\infty,\ y\rightarrow x$

b)

As x goes to the right, y approaches the asymptote y = x.
As

x\rightarrow+\infty,\ y\rightarrow x

c)

As x goes to the left, y goes down.
As $x\rightarrow-\infty,\ y\rightarrow-\infty$

d)

As x goes to the right, y goes up.
As $x\rightarrow+\infty,\ y\rightarrow+\infty$

84.

Define Asymptotic Behavior

a)

It describes the function's direction as it approaches the asymptote it curves towards $\pm$ infinity.

b)

its just crazy

85.

What is the asypmtotic behavior of this rational function?

a)

As x approaches 3 from the left, y goes down

As $x\rightarrow3^-,\ y\rightarrow-\infty$

b)

As x approaches 3 from the left, y goes up
As

x\rightarrow3^-,\ y\rightarrow+\infty

c)

As x approaches 3 from the right, y goes down
As $x\rightarrow3^+,\ y\rightarrow-\infty$

d)

As x approaches 3 from the right, y goes up
As $x\rightarrow3^+,\ y\rightarrow+\infty$

86.

What is the asypmtotic behavior of this rational function?

a)

As x approaches 0 from the left, y goes down

As $x\rightarrow0^-,\ y\rightarrow-\infty$

b)

As x approaches 0 from the left, y goes up
As

x\rightarrow0^-,\ y\rightarrow+\infty

c)

As x approaches 0 from the right, y goes down
As $x\rightarrow0^+,\ y\rightarrow-\infty$

d)

As x approaches 0 from the right, y goes up
As $x\rightarrow0^+,\ y\rightarrow+\infty$

87.

What is the asypmtotic behavior of this rational function as x approaches x = -2?

a)

As x approaches -2 from the left, y goes down

As $x\rightarrow-2^-,\ y\rightarrow-\infty$

b)

As x approaches -2 from the left, y goes up
As

x\rightarrow-2^-,\ y\rightarrow+\infty

c)

As x approaches -2 from the right, y goes down
As $x\rightarrow-2^+,\ y\rightarrow-\infty$

d)

As x approaches -2 from the right, y goes up
As $x\rightarrow-2^+,\ y\rightarrow+\infty$

88.

The set of y-values or outputs for your rational function is called the...

a)

Domain

b)

Range

c)

intervals

d)

intercepts

89.

What is the range of this rational function?

a)

$y\ne2$

b)

$\left(-\infty,+\infty\right)$

c)

$y\ne1$

90.

What is the range of this rational function?

a)

$\left[0,\infty\right)$

b)

$\left(-\infty,+\infty\right)$

c)

$\left(0,\infty\right)$

91.

What is the range of this rational function?

a)

$y\ne0$

b)

$\left(-\infty,+\infty\right)$

c)

$\left(-\infty,-0.44\right)\cup\left(0,\infty\right)$

92.

What is the range of this rational function?

a)

$y\ne1$

b)

$\left(-\infty,+\infty\right)$

c)

$y\ne-1,1$

93.

What is the range of this rational function?

a)

$y\ne x$

b)

$\left(-\infty,+\infty\right)$

c)

$y\ne0$

94.

For what value(s) of $m$ is the expression $\frac{m^2-2m+1}{2m^2+m-3}$ undefined?

a)

$-\frac{3}{2},\ 0,\ 1$

b)

$-1,\ \frac{3}{2}$

c)

$-\frac{3}{2},\ 1$

d)

$\frac{3}{2}$

95.

Solve $\frac{n}{n-4}+n=\frac{12-4n}{n-4}$

a)

$n=-4,\ n=3$

b)

$n=-3,\ n=4$

c)

$n=-4$

d)

$n=3$

96.

Solve the following equation for x:
$\frac{12}{x}+\frac{3}{4}=\frac{3}{2}$

a)

16

b)

4

c)

5

d)

8

97.

Solve for w:
$\frac{4}{w-2}=\frac{-1}{w+3}$

a)

2

b)

-2

c)

4

d)

-4

98.

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

a)

1

b)

2

c)

-1

d)

No Solution

99.

Solve: $\frac{4}{x^2-4}-\frac{2}{x}=\frac{x+2}{x^2-4}$

a)

$x=-\frac{4}{3}$

b)

$x=2$

c)

$x=-\frac{4}{3\ }\ ,\ 2$

d)

No Solution

100.

You can find the holes in the graph by setting the ____________ equal to 0 and solving for x.

a)

Numerator

b)

Denominator

c)

Canceled Factors

d)

None of the Above

101.

If the degree of the numerator is greater that the degree of the denominator the Horizontal Asymptote is

a)

$y=0$

b)

$y=1$

c)

There is no H.A.

d)

$y=\frac{L.C.\ of\ num.}{L.C.\ of\ den.}$

102.

You can find the Vertical Asymptote by setting the ____________ equal to 0 and solve for x.

a)

Numerator

b)

Denominator

c)

Canceled Factor

d)

None of the Above

103.

You can find the x-intercept by setting the _______________ equal to 0 and solving for x.

a)

Numerator

b)

Denominator

c)

Canceled Factor

d)

None of the Above

104.

$\frac{5x-10}{x^2-4}$ What is the hole:

a)

There's no Hole

b)

$\left(-2\ ,\ 0\right)$

c)

$\left(2,\ 0\right)$

d)

$\left(2,\ \frac{5}{4}\right)$

105.

$\frac{5x-10}{x^2-4}$ What are the vertical and Horizontal Asymptote of

a)

$x=-2,\ 2\ ;\ y=5$

b)

$x=-2\ ;\ y=0$

c)

$x=-2\ ;\ y=\frac{5}{2}$

d)

$x=-2\ ;\ y=5$

106.

The domain of a rational function excludes what?

a)

Vertical Asymptote and x value in the hole

b)

Vertical Asymptote and x- intercept

c)

Vertical Asymptote, Horizonal Asymptote, and x value of the hole

d)

Vertical Asymptote, x- intercept, and x value of the hole

107.

The range of a rational function excludes what?

a)

Vertical Asymptote, Horizontal Asymptote, y value in the hole

b)

Horizontal Asymptote, y- intercept, y- value in the hole

c)

Vertical Asymptote and Horizontal Asymptote

d)

Horizontal Asymptote and y value in the hole

108.

What is the hole: $\frac{x^2+4x-32}{x^2-5x+4}$

a)

$\left(4,\ 0\right)$

b)

$\left(-4,\ \frac{4}{5}\right)$

c)

$\left(4,\ 4\right)$

d)

$\left(-4,\ 0\right)$

109.

Solve for x.

a)

2

b)

18/5

c)

26/5

d)

6

110.

Solve :

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

111.

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

112.

Solve for x: $\frac{2}{x+2}+\frac{5}{x-2}=\frac{6}{x^2-4}$

a)

7

b)

6

c)

14

d)

0

113.

A water tanks is being emptied by two drains and can be emptied in 55 minutes. One drain can empty the tank in 80 minutes. Check the true statements about the drains.

a)

$\frac{1}{55}=\frac{1}{80}+\frac{1}{x}$

b)

$\frac{1}{55\ }+\frac{1}{80}=\frac{1}{x}$

c)

The second pipe can drain the pool in 176 minutes

d)

The second pipe can drain the pool in 33 minutes

114.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

115.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

116.

a)

A

b)

B

c)

C

d)

D

rational test review

Total questions: 116

Worksheet time: 5hrs 27mins

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