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

51.
53.
55.
hx
(a) Domain: all real numbers x except x 0
x2 4 4
x
x x
(b) Intercepts:
(c) Vertical asymptote: x 0
Slant asymptote: y x
(d)
(−2, 0)
fx
(a) Domain: all real numbers x except x 0
(b) No intercepts
(c) Vertical asymptote: x 0
Slant asymptote: y 2x
(d)
2x2 1
2x
x
1
x
x 4 2 2 4 6
f x
2
33
4
6
4
2
y = 2x
−6 −4 −2 2 4 6
−6
2, 0, 2, 0
−6 −4
(2, 0) 6
−2
−4
−6
y
y
y = x
9
2
9
2
x
x
33
4
73
6
52.
54.
(b) No intercepts
fx
Section 2.6 Rational Functions 215
(c) Vertical asymptote: x 0
Slant asymptote: y x
(d)
x 3 1 1 3
x 3 2 1 1 2 3
y
5
3
3
3
gx
(a) Domain: all real numbers x except x 0
x2 1 1
x
x x
(b) No intercepts
(c) Vertical asymptote: x 0
Slant asymptote: y x
5
3
(d)
gx
(a) Domain: all real numbers x except x 0
x2 5 5
x
x x
(a) Domain: all real numbers x except x 0
(b) x-intercepts: 1, 0, 1, 0
(c) Vertical asymptote: x 0
Slant asymptote: y x
(d)
y
−6 −4 −2 2 4 6
−2
−4
x
1 x2
x
f x
14
3
6
35
6
y = −x
8
6
4
2
(−1, 0) (1, 0)
−8 −6 −4 −2 4 6 8
−4
−6
−8
6
4
2
x 1
x
y
y
9
2
4
15
4
6
y = x
2
3
2
x 4
2 2 4 6
gx
17
4
5
2
5
2
17
4
37
6
x
6
x
9
2
2 4 6
3
2
14
3
6
4
2
15
4
35
6
−6 −4 −2 2 4 6
−6
y
y = x
x