C H A P T E R 2 Polynomial and Rational Functions

80. (a)
81. False. Polynomial functions do not have vertical
asymptotes.
83. Vertical asymptote: None ⇒ The denominator is not
zero for any value of x (unless the numerator is also zero
there).
Horizontal asymptote: y 2 ⇒ The degree of the
numerator equals the degree of the denominator.
fx is one possible function. There are many
correct answers.
2x2
x2 1
Section 2.6 Rational Functions 221
82. False. The graph of f x crosses y 0, which
is a horizontal asymptote.
x
x2 1
84. Vertical asymptotes:
are factors of the denominator.
Horizontal asymptotes: The degree of the
numerator is greater than the degree of the denominator.
x
f x
is one possible function. There are
many correct answers.
3
x 2, x 1 ⇒ x 2x 1
None ⇒
x 2x 1
85. x 2 15x 56 x 8x 7 86. 3x 2 23x 36 3x 4x 9
87.
(b) S
The sales in 2008 is estimated to be $763,810,000.
5.816182 130.68
0.004182 763.81
1.00
(c) Probably not. The graph has a horizontal asymptote at
Future sales may exceed this limiting value.
x3 5x2 4x 20 x 5x2 4 88. x3 6x2 2x 12 x2x 6 2x 6
x ≥ 10
3
x 5x 2ix 2i
89. 10 3x ≤ 0 10
3
90. 5 2x > 5x 1
3x ≥ 10
x
5 2x > 5x 5
91.
600
8
0
12 < 4x < 28
3 < x < 7
13
0
1 2 3 4 5 6
4x 2 < 20 92.
−3
20 < 4x 8 < 20 −4 −2 0 2
93. Answers will vary.
4 6
7
8
x
S 5.816
1454 million dollars.
0.004
1
2
7x > 0
x < 0
2x 3 ≥ 5
2x 3 ≥ 10
2x 3 ≤ 10
2x ≤ 13
x ≤ 13
2
or
x 6x 2 2
x 6x 2x 2
2x 3 ≥ 10
−3 −2 −1 0 1 2 3
2x ≥ 7
x ≥ 7
2
−8
13
−
2
−6
−4
−2
0
2
7
2
4
x
x