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

60. gx
(a) Domain: all real numbers x except x ±2
x3
2x2 1 4x
x
8 2 2x2 8
62.
(b) Intercept:
(c) Vertical asymptotes:
(d)
fx
(a) Domain: all real numbers x except x 2
5
(b) y-intercept: 0, 2
(c) Vertical asymptote: x 2
Slant asymptote: y 2x 1
2x2 5x 5
2x 1
x 2
3
x 2
(d)
Slant asymptote:
x
gx
x
y
6
107
8
15
12
9
6
3
3
38
5
−9 −6 −3 3 6 9 12 15
(( 0, − 5
(0, 0)
2
−9
y
8
6
4
0, 0
6
27
8
−8 −6 −4 4 6 8
y
y = 2x − 1
y 1
2 x
4
8
3
y =
1
x
2
x ±2
1
1
6
x
1 3 6 7
2
x
8
1 4 6
1
6
47
4
8
3
68
5
27
8
61.
63.
Section 2.6 Rational Functions 217
fx
(a) Domain: all real numbers x except x 1
x2 x 1 1
x
x 1 x 1
(b) y-intercept:
(c) Vertical asymptote: x 1
Slant asymptote: y x
(d)
f x 2x3 x 2 2x 1
x 2 3x 2
(a) Domain: all real numbers except and
(b) intercept:
intercepts:
(c) Vertical asymptote: x 2
Slant asymptote: y 2x 7
1
, 0 , 1, 0
2 x-
2x 7
x x 1 x 2
1
y- 0, 2
15
, x 1
x 2
(d)
2x 1x 1x 1
x 1x 2
2x 1x 1
, x 1
x 2
2x2 3x 1
x 2
x
y
8
6
4
2
(0, −1)
−4 −2 2 4 6 8
−4
y
4
45
2
0, 1
x 4
2 0 2 4
f x
21
5
18
3
28
12 (0, 0.5)
6 (1, 0)
x
−6 −5 −4 −3 −1
3
−12 (0.5, 0)
−18
−24
−30
−36
y = 2x − 7
y
7
3
y = x
1
3
2
x
3
13
3
0 1
1
20 2 0