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Worksheets

Simplifying Exponents & Rational Functions

Total questions: 152

Worksheet time: 13hrs 21mins

Name
Class
Date
1.
According to exponent rules, when we divide the expressions we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
2.

When you have a power to a power you __________________________________ the exponents.

a)

Divide

b)

Multiply

c)

Add

d)

Subtract

3.

To turn a negative exponent positive you


______________________.

a)

Multiplying

b)

Change the negative to positive

c)

Flip it

d)

Adding

4.

(2a2 b)(4ab2)\left(2a^2\ b\right)\left(4ab^2\right)  

a)

6a2b36a^2b^3  

b)

6a3b26a^3b^2  

c)

8a3b38a^3b^3  

d)

8a2b28a^2b^2  

5.

(2x2y3)2\left(2x^2y^3\right)^2  

a)

22x4y52^2x^4y^5  

b)

2x4y52x^4y^5  

c)

4x2y54x^2y^5  

d)

4x4y64x^4y^6  

6.
-4x0
a)
-4x
b)
-4
c)
1
d)
-1
7.
a)
2 / x2
b)
-2x2
c)
2x2
d)
2x14
8.

18c23c3\frac{18c^2}{-3c^3}  

a)

6c\frac{6}{c}  

b)

6c-6c^{ }  

c)

6c\frac{-6}{c}  

d)

183c\frac{18}{-3c}  

9.

Simplify the expression   

a)

  13x5y7\frac{-1}{3x^5y^7}  

b)

3x5y73x^5y^7   

c)

16x13y916x^{13}y^9   

d)

116x13y9\frac{1}{16x^{13}y^9}   

10.

(3m2n7m)5\left(\frac{3m^2n^7}{m}\right)^5  

a)

15m7n1215m^7n^{12}  

b)

243m5n35243m^5n^{35}  

c)

15m15n3515m^{15}n^{35}  

d)

243m7n12243m^7n^{12}  

11.
a)

25x8y225x^8y^2  

b)

10x8y210x^8y^2  

c)

10x2y6-10x^2y^6  

d)

25x2y825x^2y^8  

12.

x2x10y8\frac{x^{-2}}{x^{-10}y^{-8}}  

a)

x8y8\frac{x^8}{y^{-8}}  

b)

x20y8x^{20}y^8  

c)

x8y8x^8y^8  

d)

x10y8x2\frac{x^{10}y^8}{x^2}  

13.
a)

8xy7-8xy^7  

b)

32x2y10-32x^2y^{10}  

c)

32x10y232x^{10}y^2  

d)

16x2y1016x^2y^{10}  

14.
a)
2a2b6
b)
1/2a2b6
c)
b6/2a2
d)
2b6/a2
15.

What is the area of the rectangle with the given sides?

a)

7x3y8z47x^3y^8z^4  

b)

10x2y16z310x^2y^{16}z^3  

c)

10x3y8z410x^3y^8z^4  

d)

none of the above

16.
Which number is the BASE?
2= 8
a)
2
b)
3
c)
8
17.
Which number is the EXPONENT?
42 = 16
a)
4
b)
2
c)
16
18.
Simplify the expression x5x7
a)
x35
b)
x12
c)
x2
d)
x-2
19.
Evaluate the expression using the quotient rule.
a)
x13
b)
x5
c)
x36
d)
x-5
20.
SImplify:
32 × 333 =
a)
366
b)
333
c)
335
d)
3-31
21.
a)
y3/8
b)
y3/24
c)
y/24
d)
y3/83
22.
a)
a
b)
b
23.
Simplify (8y3)6
a)
8y18
b)
86y18
c)
48y18
d)
8y9
24.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
25.
Evaluate the expression using the quotient rule.
a)
34
b)
1/34
c)
3-12
d)
332
26.
(22y3)5
a)
27y8
b)
256y8
c)
1024y15
d)
None
27.
Simplify (x14)3
a)
x17
b)
x42
c)
x11
d)
3x14
28.
Evaluate the expression using the quotient rule.
a)
y15
b)
y50
c)
y2
d)
y5
29.
(53x2y4)0
a)
5xy
b)
1
c)
0
d)
5
30.
Simplify (-4r5)(2r8)
a)
-8r13
b)
-2r13
c)
-8r40
d)
-2y40
31.
a)
2a2b6
b)
1/2a2b6
c)
b6/2a2
d)
2b6/a2
32.
(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)
33.
20x³/(5x+10)
a)
A.4x³/(x+2)
b)
B.4x³/(x+10)
c)
C.2x³/(5x+1)
d)
D. 2x³/(x+5)
34.
(-x-5)/(x²+12x+35)
a)
A. 1/(x+7)
b)
B. 1/(x-7)
c)
C. -1/(x+7)
d)
D. -1/(x+6)
35.
Simplify by cancelling
a)
1
b)
-1
c)
Can't be simplified
36.
Which of the following is equivalent?
(7-m)
a)
(m-7)
b)
-(m+7)
c)
-(7+m)
d)
-(m-7)
37.
Simplify
a)
(x-9)/(x+9)
b)
1/(x-9)
c)
(x+9)
d)
1/(x+9)
38.
Simplify.
a)
A.
b)
B.
c)
C.
d)
D.
39.
Simplify
(x2-49)/(x2+9x+14)
a)
(x-7)/(x+2)
b)
(x+7)/(x+2)
c)
(x-7)/(x-2)
d)
(x+7)/(x+2)
40.
Simplify
(x2+6x+8)/(x2-x-6)
a)
(x+2)/(x-3)
b)
(x+4)/(x+2)
c)
(x+4)/(x-3)
d)
(x+2)/(x+2)
41.

Simplify

(8x + 32)/( x+4)

a)

8/(x - 4)

b)

-x/(x - 4)

c)

-8

d)

8

42.
(4 - x2) / (x2 - x - 2)
a)
4 / (-x - 2)
b)
-2 / (-X - 1)
c)
-1(x + 2) / (x + 1)
43.
What is the excluded value: 
7 / (x - 3)
a)
7
b)
There is not one.
c)
3
44.
(5x2 + 21x + 4) / (25x + 100)
a)
(x2 + 21x + 1) / (5x + 25)
b)
5x2 + 4 / 4x + 25
c)
(5x + 1) / 25
45.
Which value of x makes the expression undefined?
a)
-2
b)
2
c)
-6
d)
-3
46.
Simplify
(2x2-98)/(2x2+18x+28)
a)
(x-7)/(x+2)
b)
(x+7)/(x+2)
c)
(x-7)/(x-2)
d)
(x+7)/(x+2)
47.

Simplify:  x8y12x4y15Simplify:\ \ \frac{x^8y^{12}}{x^4y^{15}}  

a)

x4y3\frac{x^4}{y^3}  

b)

x12y3\frac{x^{12}}{y^3}  

c)

x12y27x^{12}y^{27}  

d)

y3x4\frac{y^3}{x^4}  

48.

Simplify: 5a3c1020a5c4Simplify:\ \frac{5a^3c^{10}}{20a^5c^4}  

a)

4c6a2\frac{4c^6}{a^2}  

b)

1a2c64\frac{1a^2c^6}{4}  

c)

1c64a2\frac{1c^6}{4a^2}  

d)

1a24c6\frac{1a^2}{4c^6}  

49.

Simplify:  8w3y11(4w3y5)2Simplify:\ \ \frac{8w^3y^{11}}{\left(4w^3y^5\right)^2}  

a)

2yw3\frac{2y}{w^3}  

b)

1y2w3\frac{1y}{2w^3}  

c)

y4w2\frac{y^4}{w^2}  

d)

1y212w9\frac{1y^{21}}{2w^9}  

50.

Simplify: 30x5y86x5y9Simplify:\ \frac{-30x^5y^8}{6x^5y^9}  

a)

15y\frac{1}{5y}  

b)

5y-5y  

c)

5x10y17-5x^{10}y^{17}  

d)

5y\frac{-5}{y}  

51.

Simplify:  x4y7x2y3Simplify:\ \ \frac{x^{-4}y^7}{x^2y^{-3}}  

a)

y10x6\frac{y^{10}}{x^6}  

b)

x6y10\frac{x^6}{y^{10}}  

c)

y4x2\frac{y^4}{x^2}  

d)

x2y4\frac{x^2}{y^4}  

52.

Simplify:   24a3c48a2c3Simplify:\ \ \ \frac{24a^3c^4}{8a^{-2}c^{-3}}  

a)

16ac16ac  

b)

3ac3ac  

c)

3a5c73a^5c^7  

d)

3a5c7\frac{3}{a^5c^7}  

53.

 2x(x2)(x2)(x+5)\ \frac{2x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}

 State the values of x which must be excluded to prevent division by zero.

a)

-2 and 5

b)

2 and -5

c)

0, 2, and -5

d)

0, -2, and 5

54.

(x + 1)(x4)(x4)(x+7)\frac{\left(x\ +\ 1\right)\left(x-4\right)}{\left(x-4\right)\left(x+7\right)}  
State the values of x that must be excluded to prevent division by zero.

a)

-1, 4, and -7

b)

-1 and 4

c)

-4 and 7

d)

4 and -7

55.

(x3)(x+4)x(x3)\frac{\left(x-3\right)\left(x+4\right)}{x\left(x-3\right)}  
State the values of x that must be excluded to prevent division by zero.

a)

0 and 3

b)

0 and -3

c)

3 and -4

d)

0, 3, and -4

56.

Simplify:  x2+6x7x249Simplify:\ \ \frac{x^2+6x-7}{x^2-49}  

a)

x1x+7\frac{x-1}{x+7}  

b)

x+1x+7\frac{x+1}{x+7}  

c)

x1x7\frac{x-1}{x-7}  

d)

x+1x7\frac{x+1}{x-7}  

57.

Simplify:  x2+6xx2+3x18Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}  

a)

xx+3\frac{x}{x+3}  

b)

xx3\frac{x}{x-3}  

c)

x+6x3\frac{x+6}{x-3}  

d)

xx+6\frac{x}{x+6}  

58.

Simplify:  x2+7x+10x24Simplify:\ \ \frac{x^2+7x+10}{x^2-4}  

a)

x5x+2\frac{x-5}{x+2}  

b)

x5x2\frac{x-5}{x-2}  

c)

x+5x+2\frac{x+5}{x+2}  

d)

x+5x2\frac{x+5}{x-2}  

59.

Simplify:  x225x26x+5Simplify:\ \ \frac{x^2-25}{x^2-6x+5}  

a)

x+5x1\frac{x+5}{x-1}  

b)

x5x1\frac{x-5}{x-1}  

c)

x+5x+1\frac{x+5}{x+1}  

d)

x5x+1\frac{x-5}{x+1}  

60.

Simplify:  x2+7x+12x2+4xSimplify:\ \ \frac{x^2+7x+12}{x^2+4x}  

a)

x+3x+4\frac{x+3}{x+4}  

b)

x3x\frac{x-3}{x}  

c)

x+3x\frac{x+3}{x}  

d)

x+3x2\frac{x+3}{x^2}  

61.

Simplify:   x24x45x281Simplify:\ \ \ \frac{x^2-4x-45}{x^2-81}  

a)

x+5x9\frac{x+5}{x-9}  

b)

x+5x+9\frac{x+5}{x+9}  

c)

x5x9\frac{x-5}{x-9}  

d)

x5x+9\frac{x-5}{x+9}  

62.

State the excluded values.

44p+20\frac{4}{4p+20}  

a)

-5

b)

-8/7

c)

No excluded values

d)

0, -3

63.

State the excluded values.

x74x28\frac{x-7}{4x-28}  

a)

1, -2

b)

0,-2

c)

9

d)

7

64.

State the excluded values.

a+7a2+4a21\frac{a+7}{a^2+4a-21}  

a)

3, -7

b)

9

c)

9, 3

d)

-5/2

65.

Simplify the rational expression.

a)
b)
c)
d)
66.

Simplify the rational expression.

a)
b)
c)
d)
67.

Simplify the rational expression and state the excluded values.

a)
b)
c)
d)
68.

Simplify the rational expression.

a)
b)
c)
d)
69.

Simplify the rational expression.

a)
b)
c)
d)
70.

Solve for x:  532x=8x\frac{5}{3}-\frac{2}{x}=\frac{8}{x}  

a)

2

b)

18/5

c)

26/5

d)

6

71.

Solve the equation for x: 2x+2+5x 2=6x24\frac{2}{x+2}+\frac{5}{x\ -2}=\frac{6}{x^2-4}  

a)

7

b)

6

c)

14

d)

0

72.

Solve for x:  5x2+x6x22x=1x\frac{5}{x-2}+\frac{x-6}{x^2-2x}=\frac{1}{x}  

a)

x = 5

b)

x = 45\frac{4}{5}

c)

x = 1

d)

x = - 4

73.

Solve: 2x21x+1=2x2x2\frac{2}{x-2}-\frac{1}{x+1}=\frac{2}{x^2-x-2}  

a)

x = 2

b)

x = -2

c)

x = 6

d)

x = 3

74.

Solve x23x=13x+2\frac{x-2}{3x}=\frac{1}{3x}+2  

a)

0

b)

35-\frac{3}{5}  

c)

-2

d)

15-\frac{1}{5}  

75.

Solve for y y+23y14=23\frac{y+2}{3}-\frac{y-1}{4}=\frac{2}{3}  

a)

y = -9

b)

y = -3

c)

y=1

d)

y = 3

76.

2n+16n8=12n1612\frac{2n+16}{n-8}=\frac{1}{2n-16}-\frac{1}{2}  

a)

235-\frac{23}{5}  

b)

77  

c)

4-4  

d)

43\frac{4}{3}  

77.

7x49x2+8x+12=3x+6+1x+2\frac{7x-49}{x^2+8x+12}=\frac{3}{x+6}+\frac{1}{x+2}  

a)

2-2  

b)

55  

c)

66  

d)

613\frac{61}{3}  

78.

1a+1=4a+12a2+a+1a\frac{1}{a+1}=\frac{4a+12}{a^2+a}+\frac{1}{a}  

a)

134-\frac{13}{4}  

b)

7, 1-7,\ 1  

c)

1-1  

d)

77  

79.

5k+7=1k+3+2k2k2+10k+21\frac{5}{k+7}=\frac{1}{k+3}+\frac{2k-2}{k^2+10k+21}  

a)

22  

b)

11  

c)

5-5  

d)

55  

80.

1x+3=3x+27x2+5x+6\frac{1}{x+3}=\frac{3}{x+2}-\frac{7}{x^2+5x+6}  

a)

5

b)

00  

c)

88  

d)

33  

81.
a)
x = 2
b)
x = 3/4
c)
x = 4
d)
x = 1/2
82.
Solve for r
a)
5
b)
- 5, 4
c)
- 5
d)
5, 4
83.

Solve for x

a)

1/3

b)

-5.5

c)

5.5

d)

2.5

84.

Solve for x

a)

4

b)

2

c)

-2

d)

-4

85.
Solve the equation for x.
a)
7
b)
6
c)
14
d)
0
86.

Solve.

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

87.

Solve.

a)

x = 4.5

b)

x = -4.5

c)

x = 3

d)

x = -3

88.
Solve the equation for x.
a)
6
b)
12
c)
0
d)
3
89.
Solve for x
a)
x = 10
b)
x = -30/13
c)
x = 6
d)
no solution
90.
Solve!
a)
x = 2
b)
x = 6
c)
x = 4
d)
x = 8
91.
Solve by cross-multiplying.
a)
x = 2
b)
No Solution
c)
x = -10
d)
x = 10
92.
a)
x = -1
b)
x = 1
c)
x = -9
d)
x = 9
93.
a)
x = 8.9
b)
x = 16
c)
x = 9
d)
x = 12
94.
a)
x = 2
b)
x = 3/4
c)
x = 4
d)
x = 1/2
95.
a)

3/5

b)

3/4

c)

1/4

d)

4/5

96.
a)

2

b)

1

c)

-1

d)

-4

97.

Solve for x

a)

x = 10

b)

x = 3013-\frac{30}{13}

c)

x = 6

d)

no solution

98.

Solve the equation for x.

a)

x = 6

b)

x = 12

c)

x = 0

d)

x = 3

99.
Solve by cross-multiplying.
a)
x = 2
b)
No Solution
c)
x = -10
d)
x = 10
100.

Solve for x.

a)

x = 2

b)

x = 185\frac{18}{5}

c)

x = 265\frac{26}{5}

d)

x = 6

101.
Solve and check for extraneous solutions
a)
x=5
b)
x= -5
c)
No Solution
102.

Solve and check for extraneous solutions

a)

x= - 3 &x= -8

b)

x= -3

c)

No Solution

d)

x= -8

103.
a)

m = 1

b)

m = 13\frac{1}{3}

c)

m = 2

d)

m = 23\frac{2}{3}

104.
Solve
a)
A
b)
B
c)
C
d)
D
105.
Solve
a)
A
b)
B
c)
C
d)
D
106.

Solve

a)

No Solution

b)

x = 6

c)

x = 7

d)

x = 5

107.

How do you determine the vertical asymptote(s) of a rational function?

a)

Calculate the average of the x-intercepts of the function.

b)

Find the values of x that make the numerator of the function equal to zero.

c)

Find the values of x that make the denominator of the function equal to zero.

d)

Look for the x-values where the function is undefined.

108.

What is the significance of a vertical asymptote in graphing rational functions?

a)

It indicates the x-intercept of the function.

b)

It represents the values where the function becomes undefined.

c)

It represents the maximum value of the function.

d)

It shows the points where the function is continuous.

109.

What does a horizontal asymptote represent in the graph of a rational function?

a)

It represents the average value of the function

b)

It represents the behavior of the function as the input values become very large or very small.

c)

It represents the x-intercept of the function

d)

It represents the maximum value of the function

110.

How do you find the slant asymptote(s) of a rational function?

a)

Take the square root of the numerator to find the slant asymptote

b)

Multiply the numerator by the denominator to find the slant asymptote

c)

Subtract the denominator from the numerator to find the slant asymptote

d)

Divide the numerator by the denominator using long division obtain the equation of the slant asymptote.

111.

Find the domain of the rational function f(x)=xx225f(x)=\frac{x}{x^2-25}

a)
(- infinity, -5) U (5, infinity)
b)
(-infinity, -5) U (-5, 5) U (5, infinity)
c)
(- infinity, 5) U (5, infinity)
d)
(- infinity, 25) U (25, infinity)
112.

State the end behavior asymptote:  
2x25x+1x2x\frac{2x^2-5x+1}{x^2-x}

a)
y = 2
b)
y = 1
c)
y = 0
d)
There is no EBA
113.

Determine the x-coordinate of the hole on the graph of 
f(x)=x22x+1x2+2x3f(x)=\frac{x^2-2x+1}{x^2+2x-3}

a)
-1
b)
3
c)
1
d)
-3
114.

State the vertical asymptotes:  
f(x)=22x2+3x5f(x)=\frac{2}{2x^2+3x-5}

a)
x = 1 , x = -5
b)
x = 1, x = -5/2
c)
x = -1/2, x = 5
d)
x = 0 , x = -5/2
115.

What is the slant asymptote of
f(x)=4x2+3x9x5f(x)=\frac{4x^2+3x-9}{x-5}  ?

a)
y = 4x - 17
b)
none
c)
y = 4x + 23
d)
x = 5
116.

What are the horizontal and vertical asymptotes?
f(x)=3x+1x1f(x)=\frac{3x+1}{x-1}

a)
x=-1 y = -3
b)
x=1 y = -3
c)
x=-1 y =3
d)
x=1, y=3
117.

What are the x-intercept(s) for the function
f(x)=4x+12x6f(x)=\frac{4x+12}{x-6}

a)
(-3,0)
b)
(6,0)
c)
(0,-2)
d)
(4,0)
118.
Name any holes of the function.
a)
x=0
b)
none
c)
x=3
d)
x=-3
119.
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
120.
Solve:
a)
(0,4]
b)
(−∞,0) U [4,∞)
c)
(−∞,0)
d)
[4,∞)
121.
Solve:
a)
(1,3]
b)
[1,3)
c)
(1,3)
d)
[1,3]
122.
a)
b)
c)
d)
123.
a)
b)
c)
d)
124.
a)
b)
c)
d)
125.
a)
b)
c)
d)
126.
a)
b)
c)
d)
127.
Determine the x-coordinate of the hole on the graph of 
f(x)= (x2-2x + 1)/(x2+2x - 3)
a)
-1
b)
3
c)
1
d)
-3
128.
State the vertical asymptotes:  
f(x) = 2 / (2x2+3x - 5)
a)
x = 1 , x = -5
b)
x = 1, x = -5/2
c)
x = -1/2, x = 5
d)
x = 0 , x = -5/2
129.
Which asymptote(s) are determined by looking at the denominator?
a)
vertical
b)
horizontal
c)
end behavior
d)
none
130.
The y-intercepts of a rational function are:
a)
the value of f(0)
b)
the real zeros of the numerator
c)
always zero
d)
the real zeros of the denominatior
131.
Name any holes of the function.
a)
x=0
b)
none
c)
x=3
d)
x=-3
132.
Solve and check for extraneous solutions.
a)
x=-1, x=-3 extraneous
b)
x=-1 extraneous, x=-2
c)
x=-1, x=-2 extraneous
d)
x=-1, x=2 extraneous
133.
a)
All Reals Except 0
b)
All Reals
c)
All Reals Except -3
d)
All Reals Except 0 and -3
134.
Match the graph to the correct rational equation below.
a)
f(x)=-8/(x+2)  +  2
b)
f(x)=8/(x-2)  +  2
c)
f(x)=1/(x+2)  +  2
d)
f(x)=-1/(x+2)  -  2
135.
What are the asymptotes?
a)
x=-1 y = -3
b)
x=1 y = -3
c)
x=-1 y =3
d)
x=1, y=3
136.
Find the vertical asymptote(s).
a)
None
b)
x = 0
c)
x= 4
d)
x = -4, 4
137.
What is the horizontal asymptote? 
a)
x = 2
b)
y = 2
c)
x = 1
d)
y = 1
138.
What are the asymptotes?
a)
x=-3, y=1
b)
x=3, y =1
c)
x=-3, y =-1
d)
x=3 y=-1
139.

Identify the point(s) of discontinuity.

f(x)=4x6f\left(x\right)=\frac{4}{x-6}  

a)

x = 0

b)

x = 6

c)

x = -6

d)

x = 4

140.

Identify the point(s) of discontinuity.

f(x)=x+2(x3)(x+2)f\left(x\right)=\frac{x+2}{\left(x-3\right)\left(x+2\right)}  

a)

Only x = 2

b)

Only x = -2

c)

Only x = 3

d)

x = 2 and x = 3

e)

x = -2 and x = 3

141.

Identify the point(s) of discontinuity.

f(x)=x13x23f\left(x\right)=\frac{x-1}{3x^2-3}  

a)

Only x = 1

b)

Only x = -1

c)

Only x = 3

d)

x = -1 and x = 1

e)

x = 1 and x = 3

142.

Find and classify each discontinuity of the function.

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

a)

x = 5, vertical asympotoe 

b)

x = -5, hole 

c)

x = -5, vertical asymptote

d)

continuous on the domain

143.

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

144.

Determine the removable point(s) of discontuity (or holes) for the following function.

f(x)=3x6x29x+14f\left(x\right)=\frac{3x-6}{x^2-9x+14}  

a)

x = 2

b)

x = 7

c)

x = 2 and x = 7

d)

x = 0

e)

Does Not Exist

145.

Determine the vertical asymptote(s) for the following function.

f(x)=2xx7f\left(x\right)=\frac{2x}{x-7}  

a)

x = 0

b)

x = 2

c)

x = 7

d)

x = -7

e)

Does Not Exist

146.

Determine the vertical asymptote(s) for the following function.

f(x)=(x+3)(x5)(x+3)f\left(x\right)=\frac{\left(x+3\right)}{\left(x-5\right)\left(x+3\right)}  

a)

x = -3

b)

x = 5

c)

x = -3 and x = 5

d)

x = 0

e)

Does Not Exist

147.

Determine the horizontal asymptote(s) for the following function.

f(x)=2x3+5x14x32x2f\left(x\right)=\frac{2x^3+5x-1}{4x^3-2x^2}  

a)

y = 0

b)

y = 2

c)

y = 4

d)

y = 1/2

e)

Does Not Exist

148.

Determine the horizontal asymptote(s) for the following function.

f(x)=2x5x21f\left(x\right)=\frac{2x-5}{x^2-1}  

a)

y = 2

b)

y = 1

c)

y = -1

d)

y = 0

e)

Does Not Exist

149.

Determine the horizontal asymptote(s) for the following function.

f(x)=4x3x29f\left(x\right)=\frac{4x^3}{x^2-9}  

a)

y = 4

b)

y = 3

c)

y = -3

d)

y = 0

e)

Does Not Exist

150.

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

151.

Determine all removable points of discontinuity (holes), vertical asympotes, and horizontal asympotes for the following function.

f(x)=2x12x2+5x3f\left(x\right)=\frac{2x-1}{2x^2+5x-3}  

a)

Holes: x = -3
Vertical: x = 1/2
Horizontal: y = 0

b)

Holes: x = 1/2
Vertical: x = -3
Horizontal: y = 0

c)

Holes: Do Not Exist
Vertical: x = 1/2 and x = -4
Horizontal: y = 1

d)

Holes: x = 1/2
Vertical: x = -3
Horizontal: y = 1

e)

Holes: x = -3
Vertical: x = 1/2
Horizontal: Does Not Exist

152.
What are the asymptotes?
a)
x=-2 and y=-1
b)
x=-2 and y=1
c)
x=2 and y=1
d)
x=2 and y = -1