Free Printable Unit 8 (Rational Functions) Quiz #1 Review

1.

Factor and cancel out in order to simplify.

a)

9(x+10)

b)

x+10

c)

9

d)

x+9

2.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

3.

Simplify the rational function

a)

1/(x + 5)

b)

1/(x - 5)

c)

(x - 5)(x + 5)

d)

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

4.

Simplify the rational function

a)

1/(3x)

b)

3x(x + 1)

c)

3x

d)

(x + 1)

5.

Simplify.

a)

A

b)

B

c)

C

d)

D

6.

Factor out, cancel out, and write remaining terms.

a)

A

b)

B

c)

C

d)

D

7.

simplify by factoring out and canceling out.

a)

a

b)

b

c)

c

d)

d

8.

(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)

9.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

10.

Simplify (look for common factors that you can factor out and cancel out)

a)

A.4x³/(x+2)

b)

B.4x³/(x+10)

c)

C.2x³/(5x+1)

d)

D. 2x³/(x+5)

11.

Simplify

a)

(n-2)/(n+2)

b)

(n+2)/(n-2)

c)

1/(n+2)

d)

1/(n-2)

12.

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

13.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

14.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

15.

What is the horizontal asymptote of the function given?

a)

y = 2

b)

x = 1

c)

x = 2

d)

y = -1

16.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

17.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

18.

Factor the following polynomial:

$3x^2+14x-5$

a)

(3x + 5)(x - 1)

b)

(3x - 1)(x + 5)

c)

(3x + 1)(4x - 5)

d)

(x - 15)(x + 14)

19.

Simplify the following rational function:

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

a)

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

b)

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

c)

$\frac{\left(x+1\right)\left(x+2\right)}{\left(x+4\right)\left(x-2\right)}$

d)

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

20.

Simplify by factoring:

$\frac{x^2+5x-14}{x^2-4}$

a)

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

b)

$\frac{x+7}{x+2}$

c)

$\frac{x-7}{x-2}$

d)

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

21.

Simplify by factoring:

$\frac{3x^2+14x-5}{x^2+8x+15}$

a)

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

b)

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

c)

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

d)

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

22.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

23.

What are the asymptotes?

a)

x = -1 y = -3

b)

x = 1 y = -3

c)

x = -1 y = 3

d)

x = 1 y = 3

24.

Which of the following represents the graph below?

a)

b)

c)

d)

25.

Divide.

a)

undefined

b)

0

c)

15

d)

-0

26.

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

a)

vertical

b)

horizontal

c)

slant

d)

none

27.

What is the domain and range?

a)

D : $\left(-\infty,-3\right)\cup\left(-3,\infty\right)$
R: $\left(-\infty,1\right)\cup\left(1,\infty\right)$

b)

D : $\left(-\infty,1\right)\cup\left(1,\infty\right)$
R: $\left(-\infty,-3\right)\cup\left(-3,\infty\right)$

c)

D : $\left(-\infty,3\right)\cup\left(3,\infty\right)$
R: undefined

d)

D: $\left(-\infty,-1\right)\cup\left(-1,\infty\right)$
R: $\left(-\infty,3\right)\cup\left(3,\infty\right)$

28.

What is the domain and range?

a)

D:\ \left(-\infty,2\right)\cup\left(2,\infty\right)

R:\ \left(-\infty,1\right)\cup\left(1,\infty\right)

b)

$D:\ \left(-\infty,1\right)\cup\left(1,\infty\right)$
$R:\ \left(-\infty,2\right)\cup\left(2,\infty\right)$

c)

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

d)

$D:\ \left(-\infty,-2\right)\cup\left(-2,\infty\right)$
$R:\ \left(-\infty,-1\right)\cup\left(-1,\infty\right)$

29.

The rational function, $y=\frac{1}{x-5}$ is undefined at...

a)

x = 1

b)

x = 5

c)

x = -5

d)

x = 0

30.

The rational function, $y=\frac{1}{x+7}$ has a vertical asymptote at...

a)

y = -7

b)

x = 7

c)

y = 1

d)

x = -7

31.

A vertical asymptote always has the equation...

a)

x = __

b)

y = __

32.

Which rational function has a vertical asymptote at x = -3

a)

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

b)

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

c)

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

d)

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

33.

What is the equation of the rational function graphed?

a)

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

b)

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

c)

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

d)

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

34.

The rational function, $f\left(x\right)=3+\frac{2}{x-4}$ has a horizontal asymptote at...

a)

y = -4

b)

y = 2

c)

y = 3

d)

y= 4

35.

What is the equation of this rational function

a)

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

b)

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

c)

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

d)

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

36.

Which of the following is a RATIONAL FUNCTION?

a)

b)

c)

d)

37.

Which is the graph of the rational equation:

a)

b)

c)

d)

38.

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)

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

39.

What are the transformations?

a)

stretched, reflected over x, left

b)

stretched, reflected over y, right

c)

shrink, right, down

d)

shrink, left, down

40.

Describe the transformations of the function.

a)

Shift up by 2 units

Reflected over the x-axis

b)

Shift down by 2 units

Reflected over the y-axis

c)

Shift up by 2 units

Reflected over the y-axis

d)

Shift left by 2 units

Reflected over the x-axis

41.

a)

All Reals Except 0

b)

All Reals

c)

All Reals Except -3

d)

All Reals Except 0 and -3

42.

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

43.

a)

A

b)

B

c)

C

d)

D

44.

a)

A

b)

B

c)

C

d)

D

45.

a)

All Real #s; x ≠ 1

b)

All Real #s; y ≠ −1

c)

All Real #s; y ≠ 1

d)

All Real #s; x ≠ −1

46.

a)

All Real #s; x ≠ 1

b)

All Real #s; x = −1

c)

All Real #s; x ≠ -2

d)

x ≠ −2

47.

a)

A

b)

B

c)

C

d)

D

48.

a)

The function's range is All real #s, y ≠ -1

b)

The function's domain is All real #s, x ≠ -1

c)

The function has no vertical shifts

d)

The function is reflected over the x-axis

49.

What is the vertical asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

50.

Describe all transformations from the parent function g(x)=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

51.

Find the vertical asymptote(s).

a)

None

b)

x = 0

c)

x= 4

d)

x = -4, 4

52.

The value of y varies directly with x. Which function represents the relationship between x and y if y = 14 when x = 6.

a)

y=20x

b)

y=84x

c)

y=7/3x

d)

y=3/7x

53.

In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.

a)

26

b)

3

c)

58.5

d)

2

54.

Which of the following represents indirect variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

55.

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

56.

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

57.

What kind of equation is this?
xy = -18

a)

Linear Equation

b)

Direct Variation

c)

Inverse Variation

d)

Joint Variation

58.

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

59.

The cost of producing pencils varies directly with the number of pencils produced. If the cost of producing 12,800 pencils is $400, then what will be the cost of production for 15,000 pencils?

a)

$468.75

b)

$512.00

c)

$341.33

d)

$412.80

60.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

61.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

62.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

63.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

64.

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 5 cm on a side is 250 g, find the weight of the liquid in a cubical container 3 cm on a side.

a)

12 g

b)

6 g

c)

27 g

d)

54 g

65.

The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?

a)

308.05 ft

b)

295.75 ft

c)

296.09 ft

d)

253.5 ft

66.

If f varies jointly as q² and h, and f = 96 when q = 4 and h = 3, find q when f = 48 and h = 6.

a)

4

b)

2

c)

6

d)

3

67.

The frequency of a vibrating string varies inversely as its length. A string 3 feet long vibrates 175 cycles per

second. Find the frequency of a 5 foot string.

a)

105 cycles

b)

291.7 cycles

c)

2625 cycles

d)

332 cycles

68.

Suppose y varies jointly as x & z.
If y = -180 when z = 15
and x = -3,
then find y when x = 7 and z = -5.

a)

-140

b)

140

c)

-4

d)

4

69.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

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

70.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

71.

(X² + X - 20) / (X² + 2X - 15)

a)

(X - 4) / (2X - 3)

b)

(X - 4) / (X - 3)

c)

(X +4) / (X + 3)

72.

a)

A

b)

B

c)

C

d)

D

73.

Divide the Rational Expression

\frac{6}{k-4}\div\frac{k+6}{k^2+2k-24}

a)

$\frac{9}{k-4}$

b)

$\frac{k+7}{8}$

c)

$6$

d)

$k-3$

74.

a)

A

b)

B

c)

C

d)

D

75.

a)

A

b)

B

c)

C

d)

D

76.

a)

A

b)

B

c)

C

d)

D

e)

answer not here

77.

a)

A

b)

B

c)

C

d)

D

78.

What is the equivalent multiplication statement for

\frac{9}{9p-18}\div\frac{1}{p-2}

?

*Do not have to solve!

a)

$\frac{9}{9p-18}\cdot\frac{1}{p-2}$

b)

$\frac{9}{9p-18}\cdot\frac{p-2}{1}$

c)

$\frac{9p-18}{9}\cdot\frac{1}{p-2}$

d)

$\frac{9p-18}{9}.\frac{p-2}{1}$

79.

What is the equivalent multiplication statement for

\frac{y-2}{y-8}\div\frac{y^2-4}{y^2-8x+9}

?

*Do not have to solve!

a)

$\frac{y-2}{y-8}.\frac{y^2-8x+9}{y^2-4}$

b)

$\frac{y-2}{y-8}\cdot\frac{y^2-4}{y^2-8x+9}$

c)

$\frac{y-8}{y-2}\cdot\frac{y^2-4}{y^2-8x+9}$

d)

$\frac{y-8}{y-2}\cdot\frac{y^2-8x+9}{y^2-4}$

80.

Divide and simplify the result:

$\frac{a-4}{a^2-2a-8}\div\frac{1}{a-5}$

a)

$\frac{a-4}{a-5}$

b)

$\frac{a-5}{a-4}$

c)

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

d)

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

81.

Divide and simplify the result:

\frac{3x^2-14x-5}{6x+2}\div\frac{x^2-25}{x+5}

a)

$\frac{x+5}{2x-10}$

b)

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

c)

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

d)

$\frac{1}{2}$

82.

Divide and simplify the result:

\frac{2x^2+5x-3}{3x-9}\div\frac{x^2+2x-3}{x-3}

a)

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

b)

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

c)

$\frac{2}{3}$

d)

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

83.

Which of the following represent the graph?

a)

b)

c)

d)

84.

Describe the transformation of the function.

a)

shift left 3 units

b)

shift right 3 units

c)

shift up 3 units

d)

shift down 3 units

85.

Describe the transformation of the function.

a)

shift right by 3 units

b)

shift left by 3 units

c)

shift up by 3 units

d)

shift down by 3 units

86.

Describe the transformations of the function.

a)

Shifted right by 4 units

Shifted down by 7 units

Stretched Vertically

b)

Shifted right by 4 units

Shifted up by 7 units

Stretched Vertically

c)

Shifted right by 4 units

Shifted down by 7 units

Compressed Vertically

d)

Shifted left by 4 units

Shifted down by 7 units

Compressed Vertically

87.

What is the horizontal asymptote of the function?

a)

x =1

b)

x = -2

c)

x = 2

d)

y = 0

88.

What is the vertical asymptote of the function?

a)

x = 2

b)

x = -2

c)

x = 0

d)

x = 1

89.

What is the equation of the Vertical Asymptote of $y=\frac{3}{x-4}+2$

a)

$x=2$

b)

$y=2$

c)

$x=4$

d)

$y=4$

e)

No Vertical Asymptote

90.

What is this function called?

a)

Quadratic

b)

Reciprocal

c)

Polynomial

d)

Exponential

Unit 8 (Rational Functions) Quiz #1 Review

Total questions: 90

Worksheet time: 7hrs 51mins

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