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

35. gs
(a) Domain: all real numbers s
s
s2 1
37.
(b) Intercept:
(c) Horizontal asymptote:
(d)
hx x2 5x 4
x 2 4
(a) Domain: all real numbers x except x ±2
(b) x- intercepts: 1, 0, 4, 0
y-intercept:
0, 1
(c) Vertical asymptotes: x 2, x 2
Horizontal asymptote: y 1
(d)
x
y
4
10
3
2
1
(0, 0)
−1
−2
0, 0
6
4
2
y
−6 −4
(4, 0) 6
y
3
28
5
1 2
x 1x 4
x 2x 2
(1, 0)
1
10
3
y 0
s 2 1 0 1 2
gs
2
5
1
2
0
1
2
s
x
2
5
0 1 3 4
0 0
2
1
5
38.
gx x2 2x 8
x 2 9
Section 2.6 Rational Functions 211
36. fx
(a) Domain: all real numbers x except x 2
(b)
1
y- intercept: 0, 4
(c) Vertical asymptote: x 2
Horizontal asymptote: y 0
1
x 22 (d)
(a) Domain: all real numbers x except x ±3
8
(b) y- intercept: 0, 9
x-intercepts:
4, 0, 2, 0
(c) Vertical asymptotes: x ±3
Horizontal asymptote: y 1
(d)
x
y
−1
−2
−3
−4
x
y
0 1 3 4
1
4
y
(( 0, − 1
4
5
27
16
1
2
4
9
1 3
6
4
2
4
16
7
1
y
(0, 0.88)
(4, 0)
−6 −4
(−2, 0) −2
−4
−6
2 4 6
3
2
x 4x 2
x 3x 3
2
4
x
x
0 2 4 5
8
9
5
2
4
8
5
0 0
1
7
16
4
7
2
9
1
4