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

210 Chapter 2 Polynomial and Rational Functions
31.
5 2x 2x 5
Cx
1 x x 1
(a) Domain: all real numbers x except x 1
(b) x-intercept:
33. fx
(a) Domain: all real numbers x
x2
x2 9
(b) Intercept:
(c) Horizontal asymptote: y 1
(d)
y-intercept:
(c) Vertical asymptote: x 1
Horizontal asymptote: y 2
(d)
x
y
((
5
− , 0
2
−6 −4 2 4
±1
1
10
3
2
−2 −1 1 2
−1
0, 0
y
5, 0 2
0, 5
x 4 3 2 0 1 2
Cx
y
±2
6
(0, 5)
4
13
(0, 0)
1
2
1 1 5 3
±3
1
2
x
x
7
2
1 3x 3x 1
32. Px
1 x x 1
(a) Domain: all real numbers x except x 1
34.
(b) x-intercept:
1 2t 2t 1
ft
t t
(a) Domain: all real numbers t except t 0
(b) t-intercept:
(c) Vertical asymptote: t 0
Horizontal asymptote: y 2
(d)
y-intercept:
(c) Vertical asymptote: x 1
Horizontal asymptote: y 3
(d)
6
5
4
y
(0, 1) 1
, 0
3
−2 −1 2 3 4
−2 −1 1 2
−1
−3
y
1
, 0 2
t 2 1 1 2
y 3 0 1 3
2
5
2
1
, 0 3
0, 1
x 1 0 2 3
y 2 1 5 4
( )
1 ( , 0)
2
1
x
t
2