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

252 Chapter 2 Polynomial and Rational Functions
2 x 2
121. gx x
1 x x 1
(a) Domain: all real numbers x except x 1
(b) x-intercept:
y-intercept:
(c) Vertical asymptote: x 1
Horizontal asymptote: y 1
(d)
6
4
(0, 2)
(−2, 0)
−2
−4
−6
−8
y
2, 0
0, 2
x 0 2 3
y 2 5
1
1
4
2
123. px
(a) Domain: all real numbers x
x2
x2 1
(b) Intercept:
(c) Horizontal asymptote:
(d)
4
3
2
−3 −2 −1 (0, 0) 2 3
−2
y
2
0, 0
x
2
y 1
x ±3 ±2 ±1 0
9
10
4
5
1
2
y 0
125. fx
(a) Domain: all real numbers x
(d)
x
x2 1
(b) Intercept:
0, 0
(c) Horizontal asymptote: y 0
x
122.
x 3
hx
x 2
(a) Domain: all real numbers x except x 2
(b) x-intercept: 3, 0
3
y-intercept: 0, 2
(c) Vertical asymptote: x 2
Horizontal asymptote: y 1
(d)
x 1 0 1 3 4 5
y 2 0
(( 0, 3
2
5
4
3
−2 −1
−2
1 4
(3, 0)
5 6
−3
4
3
y
3
2
124. f x
(a) Domain: all real numbers x
2x
x2 4
(b) Intercept:
(c) Horizontal asymptote:
(d)
x 2
1 0 1 2
2
5
1
2
y 0
3
2
1
(0, 0)
−1
−2
−3
0, 0
y
1 2 3
x
x
1
2
y 0
x 2 1 0 1 2
y 0
1
2
1
2
2
5
2
5
2
1
(0, 0)
−1
−2
2
5
y
1
2
2
3
1 2
x