Free Printable rational function

1.

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

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

2.

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

3.

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)

4.

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

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

5.

a)

2

b)

1

c)

-1

d)

-4

6.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

7.

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

a)

x = 1

b)

x = 5

c)

x = -5

d)

x = 0

8.

What is the range of

$y=\frac{x^2+5x+6}{x+2}$ ?

a)

All real numbers except - 2

b)

All real numbers except - 1

c)

All real numbers except 1

d)

All real numbers except 2

9.

For which values of x is the function

\ f\left(x\right)\ =\ \frac{x^2\ -\ 25}{x^2\ -\ 12x\ +\ 32}not\ defined?

a)

4,8

b)

-4,-8

c)

-4,8

d)

4,-8

10.

What are/is the zero/s of the function?

a)

x= 0

b)

x= 4

c)

x= 5

d)

x= -5

11.

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

12.

What are the zeroes of the function?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

13.

Identify the given expression:

a)

Rational Equation

b)

Rational Expression

c)

Rational Function

d)

Rational Inequality

14.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

15.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

16.

Identify the given.

a)

Rational Equation

b)

Rational Inequality

c)

Rational Function

d)

Not a Rational Function

17.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

18.

Identify the given.

a)

Rational Equation

b)

Rational Inequality

c)

Rational Function

d)

Not a Rational Function

19.

Identify the given expression:

a)

Rational Equation

b)

Rational Expression

c)

Rational Function

d)

Rational Inequality

20.

Which of the following is considered as removable discontinuities?

a)

intercepts

b)

holes

c)

asymptotes

d)

domains

21.

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)

22.

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

23.

What is the horizontal asymptote of the following function?

a)

x = -2

b)

x = 2

c)

y = -3

d)

y = 3

24.

What is the vertical asymptote of the following function?

a)

x = -2

b)

x = 2

c)

y = -3

d)

y = 3

25.

What is the range for the following function?

a)

All real numbers.

b)

All real numbers except for -2.

c)

All real numbers except for 2.

d)

All real numbers exceptt for 4.

26.

What is the X-Intercept?

a)

x= 0

b)

x= 4

c)

x= 5

d)

x= -5

27.

a)

Function

b)

Not Function

28.

a)

Function

b)

Not Function

29.

a)

Function

b)

Not Function

30.

Identify the given expression:

a)

Rational Equation

b)

Rational Expression

c)

Rational Function

d)

Rational Inequality

31.

Identify the given expression:

a)

Rational Equation

b)

Rational Expression

c)

Rational Function

d)

Rational Inequality

32.

Identify the given expression:

a)

Rational Equation

b)

Rational Expression

c)

Rational Function

d)

Rational Inequality

33.

Identify the given expression:

a)

Rational Equation

b)

Rational Expression

c)

Rational Function

d)

Rational Inequality

34.

Identify the given expression:

a)

Rational Equation

b)

Rational Expression

c)

Rational Function

d)

Rational Inequality

35.

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

a)

Numerator

b)

Denominator

c)

Right side

d)

Left side

36.

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

37.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

38.

What is the horizontal asymptote?

a)

x = 2

b)

y = 2

c)

x =-2

d)

y=-2

39.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

40.

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

a)

x = 1

b)

x = 5

c)

x = -5

d)

x = 0

41.

Rational functions always have exactly 1 vertical asymptote.

a)

True

b)

False

42.

A vertical asymptote always has the equation...

a)

x = __

b)

y = __

43.

This rational function is undefined at...

a)

x = 4

b)

x = -4

c)

x = 0

d)

x = 5

44.

The domain are the ______ values.

a)

y

b)

x

c)

Both x and y

45.

The range are the _____ values.

a)

y

b)

x

c)

Both x and y

46.

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

a)

x=

b)

y=

47.

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

48.

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

49.

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

50.

$f\left(x\right)=\frac{2x^{\frac{1}{3}}+5x-4}{x-3}$

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

d)

None of These

51.

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

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

d)

None of These

52.

$f\left(x\right)=\frac{x-7}{\sqrt[]{x^3-343}}$

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

d)

None of These

53.

$\sqrt[]{x^2-4}=8$

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

d)

None of These

54.

Is there a hole on the graph of the function?

f\left(x\right)=\frac{\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-5\right)}

a)

Yes when x = 2

b)

Yes when x = -2

c)

No there are no holes.

d)

Yes when x = 5

55.

Does this function have any holes, any zeros? If so, what are they?

$y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$

a)

A hole when x = 4 No Zeros

b)

A hole when x =- 4 Zeros when: x = -3 and x = -7

c)

A hole when x = 4 Zeros when: x = -3 and x = -7

d)

A hole when x = 4 Zeros when x = 3 and x = 7

56.

What is the horizontal asymptote of the rational function $f\left(x\right)=\frac{3x^2+2x-1}{x^2-4}$ ?

a)

y=3

b)

y=2

c)

y=1

d)

y=0

57.

What is a rational function?

a)

A function with a square root.

b)

A function with a rational exponent.

c)

A function that can be expressed as a ratio of two polynomials.

d)

A function with complex roots.

58.

What is the x - intercept of the function $f\left(x\right)\ =\ \frac{1\ -\ x^2}{x^2-\ 9\ }$ ?

a)

$x\ =\ 0$

b)

$x\ =\ -\ 1$

c)

$x\ =\ -\ 1,\ x\ =\ 1$

d)

$x\ =\ 1$

59.

What is the correct graph of the function $f\left(x\right)\ =\ \frac{x\ +2}{x\ -\ 2}$ ?

a)

b)

60.

What is the y - intercept of the function $f\left(x\right)=\ \frac{x+2}{x-1}$ ?

a)

$2$

b)

$1$

c)

$-2$

d)

$-1$

61.

Find the y intercept of the function $f\left(x\right)\ =\ \frac{x^2+x\ -\ 3\ }{x^{2\ }+\ x\ -\ 12}$

a)

$\left(0,\ \frac{1}{4}\right)$

b)

$\left(0,0\right)$

c)

$\left(0,\frac{-1}{4}\right)$

d)

$\left(\frac{1}{4},\ 0\right)$

62.

What's the horizontal asymptote of the function?

$f\left(x\right)=\frac{3x+2}{x^2+1}$

a)

y = 3

b)

No horizontal asymptote

c)

y = 0

d)

y = 2

63.

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)

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

64.

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

65.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

66.

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)

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

67.

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)

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

68.

Graph the function.

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

a)

b)

c)

d)

69.

Graph the function.

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

a)

b)

c)

d)

70.

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

a)

(1, 0)

b)

(-1, 0)

c)

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

d)

(0, 0), (1, 0)

71.

What is the equation of the vertical asymptote?

a)

x = 0

b)

x = 4

c)

x = -1, x = 4

d)

x = -1

72.

What is the equation of the slant asymptote?

a)

y = x + 1

b)

y = x + 2

c)

y = x + 3

d)

y = x

73.

a)

All Real #s; x ≠ 1

b)

All Real #s; y ≠ −1

c)

All Real #s; y ≠ 1

d)

All Real #s; x ≠ −1

74.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

75.

What is the horizontal asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

76.

What are the asymptotes?

a)

x=-1 y = -3

b)

x=1 y = -3

c)

x=-1 y =3

d)

x=1, y=3

77.

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

a)

vertical

b)

horizontal

c)

end behavior

d)

none

78.

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)

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

79.

$\frac{2+x}{2-x}\ge1$

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

d)

None of These

80.

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

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

d)

None of These

81.

$y\ =\ x^2+2x+1$

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

d)

None of These

82.

$\frac{9x-13}{2x+4}=\frac{5x}{x+1}$

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

d)

None of These

83.

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

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

d)

None of These

84.

What's the vertical asymptote of the function?

a)

x = 4

b)

x = 16

c)

x = 4 , x = -4

d)

No vertical asymptote

85.

What's the vertical asymptote of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

86.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

87.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

88.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 2

d)

y = 4

89.

Given the function $f\left(x\right)\ =\ \frac{1\ -\ x^2}{x^{2\ }-\ 9\ }$ identify the vertical and horizontal asymptotes

a)

$x\ =\ -\ 3\ and\ x\ =\ 3\ ;\ y\ =\ 1$

b)

$x\ =\ -\ 3\ and\ x\ =\ 3\ ;\ y\ =\ -\ 1$

c)

$x\ =\ -1\ ;\ y\ =\ -\ 3\ and\ y\ =\ 3$

90.

Given the function $f\left(x\right)=\ \frac{x^2+x\ -\ 3}{x^2+x\ -\ 12\ }$ , identify the vertical and horizontal asymptotes

a)

$x\ =\ -\ 4\ and\ x\ =\ 3\ ;\ y\ =\ 1$

b)

$x\ =\ 4\ ,\ and\ x\ =\ -3\ ;\ y\ =\ 1$

c)

$y\ =\ -4\ and\ y\ =\ 3\ ;\ x\ =\ 1$

91.

Identify the LCD.

a)

x²(x - 2)

b)

x(x - 2)

c)

x

d)

(x - 2)

92.

Identify the LCD.

a)

(x + 5)

b)

x²(x + 5)

c)

x

d)

x(x + 5)

93.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

94.

Solve by cross-multiplying

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

95.

Simplify.

a)

A

b)

B

c)

C

d)

D

96.

a)

(x+2)/(6x²)

b)

(3x+4)/(6x²)

c)

(3x+8)/(6x²)

d)

(3x+2)/(6x²)

97.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

98.

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

99.

What is the horizontal asymptote?

a)

x = 2

b)

y = 2

c)

x =-2

d)

y=-2

100.

What is the vertical asymptote?

a)

x =-3

b)

y = -3

c)

x = 3

d)

y = 3

101.

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)

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

102.

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

103.

Given the function $f\left(x\right)\ =\ \frac{\left(x\ +\ 2\right)}{\left(x\ -\ 1\ \right)}$ , identify the vertical and horizontal asymptotes.

a)

$x\ =\ 1,\ y\ =\ 1$

b)

$x\ =\ -1,\ y\ =\ 1$

104.

Given the function $f\left(x\right)\ =\ \frac{x}{x^2-1}$ identify the vertical and horizontal asymptotes.

a)

$y\ =\ -\ 1\ and\ y\ =\ 1\ ;\ x\ =\ 0\$

b)

$x\ =\ -\ 1\ and\ x\ =\ 1\ ;\ y\ =\ 0\$

105.

Given the function $f\left(x\right)\ =\ \frac{1}{4\ -\ x^2}$ find the vertical and horizontal asymptotes

a)

$x\ =\ 2\ and\ x\ =\ -\ 2,\ y\ =\ 0\$

b)

$x\ =\ 0\ ,\ y\ =\ -2\ and\ y\ =\ 2$

106.

Find the Vertical Asymptotes for the following function

g\left(x\right)\ =\frac{2x^2+x-9}{x^2-2x-8}

a)

$x=-4,\ x=2$

b)

$x=-2,\ x=4$

c)

$x=-6,\ x\ =\ -2$

d)

$x=\ 2,\ x=6$

107.

Rewrite the following rational expression to identify the asymptotes.

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

a)

$y=2,\ x\ =-4$

b)

$y=-4,\ \ x\ =2$

c)

$y=2,\ x=4$

d)

$y=4,\ x=2$

108.

What are the asymptotes for the following rational function?

$f\left(x\right)\ =\ \frac{6x}{2x+1}$ ?

a)

$y\ =3,\ x\ =\ \frac{1}{2}$

b)

$y=-\frac{1}{2},\ x\ =\ 3$

c)

$y\ =3,\ x\ =-\frac{1}{2}$

d)

$y=\frac{1}{2},\ x\ =\ 3$ y=1/2

109.

Multiply the rational expression below.

a)

6/(x+4)

b)

(x+7)(x-4)/3(x+5)

c)

(x-4)/6

d)

(x-4)/2

110.

Multiply

a)

2x/(x-1)(x+3)

b)

3x+11/2x²+9x+5

c)

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

d)

2/(x-1)(x+3)

111.

Find and fully factor the difference between the rational functions

a)

x²+9x-18/2(x-1)(x-3)

b)

x²+9x/2(x-1)(x-3)

c)

(x+6)/2(x-1)

d)

x²+4/x²-3

112.

a)

A.

b)

B.

c)

C.

d)

D.

113.

Simplify

a)

12/(a-6)(a+6)

b)

(6a+12)/(a-6)(a+6)

c)

15a/(a-6)(a+6)

d)

(6a-12)/(a-6)(a+6)

114.

Subtract

a)

A

b)

B

c)

C

d)

D

115.

a)

A

b)

B

c)

C

d)

D

116.

a)

A

b)

B

c)

C

d)

D

117.

Divide

a)

A

b)

B

c)

C

d)

D

118.

Multiply

a)

A.

b)

B.

c)

C.

d)

D.

119.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

120.

Find the domain of the function. $f(x)=\frac{x}{2x+4}$

a)

x cannot equal to 2

b)

x cannot equal to 1/2

c)

x cannot equal to -2

d)

x cannot equal -4

121.

Find the domain of the function. $f(x)=\frac{x^3}{x+8}$

a)

x cannot equal to 8

b)

x cannot equal to 0

c)

x cannot equal to -8

d)

All real numbers

122.

What is the domain and range?

a)

D: x ≠ -3
R: y≠ 1

b)

D: x ≠ 1
R: y≠ -3

c)

D: x ≠ 3
R: y≠ 1

d)

D: x ≠ -1
R: y≠ 3

123.

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

124.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

125.

What is the horizontal asymptote of the function given?

a)

y = 2

b)

x = 1

c)

x = 2

d)

y = -1

rational function

Total questions: 125

Worksheet time: 4hrs 9mins

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