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

212 Chapter 2 Polynomial and Rational Functions
39.
f x
(a) Domain: all real numbers x except x 2, x ±1
2x2 5x 3
x3 2x2 x 2
2x 1x 3
x 2x 1x 1
(b) x-intercepts:
y-intercept:
(c) Vertical asymptotes: x 2,
x 1 and x 1
Horizontal asymptotes: y 0
(d)
1
, 0
2
9
6
3
(3, 0)
−4 −3 3 4
(( −
((
0, − 3
2
41. f x
(a) Domain: all real numbers x except x 3 and x 2
(b) Intercept: 0, 0
(c) Vertical asymptote: x 2
Horizontal asymptote: y 1
(d)
x2 3x
x2 x 6
xx 3 x
, x 3
x 3x 2 x 2
42.
5x 4
f x
x
(a) Domain: all real numbers x except x 4 or x 3
(b) y- intercept: 0, 5 3
x-intercept:
none
(c) Vertical asymptote: x 3
Horizontal asymptote: y 0
(d)
2 x 12
5x 4 5
, x 4
x 4x 3 x 3
x 1 0 1 3 4
y
1
3 0 1 3 2
x 2 0 2 5 7
6
4
2
−6 −4 −2
4 6
(0, 0)
−4
−6
y
y
0, 3
1,
0 , 3, 0
2
2
x 3 2 0 1.5 3 4
f x
3
4
5
4
3
2
x
x
48
5
0
3
10
40.
x
f x
(a) Domain: all real numbers x except x 1, x 2,
or x 3
(b) x-intercepts: 1, 0, 2, 0
y-intercept: 0, 1 3
(c) Vertical asymptotes: x 2, x 1, x 3
Horizontal asymptote: y 0
2 x 2
x3 2x2 5x 6
x 1x 2
x 1x 2x 3
(d)
x 4
3 1 0 2 4
y 0 0
( −1,
0)
((
1
0, −
3
y
6
4
2
(0, −1.66)
9
35
1
−4
−6
y
4
3
2
1
−2
−3
−4
−5
y
5
12
(2, 0)
5
3
2 4 5
5
2 4 6 8
x
x
5
2
1
3
5
4
5
9