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

218 Chapter 2 Polynomial and Rational Functions
64.
66.
68.
f x 2x3 x 2 8x 4
x 2 3x 2
(a) Domain: all real numbers except or
(b) intercept:
intercepts: 2, 0,
(c) Vertical asymptote: x 1
Slant asymptote: y 2x 7
1
x x 1 x 2
y- 0, 2
x-
, 0 2
(d)
fx
Domain: all real numbers x except x 1
2x2 x
1
2x 1
x 1 x 1
Vertical asymptote:
x 1
Slant asymptote: y 2x 1 −12
Line: y 2x 1
12 2x x2 1 2
hx x 1
24 x 2 4 x
Domain: all real numbers x except x 4
Vertical asymptote:
Slant asymptote:
Line: y 1
x 1
2
70. (a) x-intercept:
(b)
2x 7 9
, x 2
x 1
x
y
0 2x
x 3
0 2x
0 x
3
5
4
(−2, 0)
30
24
18
12
−6 −2
(0, −2)
2 4 6
y
2
((
− , 0
1
2
1
1
2
y = 2x + 7
x 4
y 1
2 x 1 −16
x
x 2x 22x 1
x 2x 1
1
2
0 3 4
0 2 10 28 18
6
−10
3
2
10
−6
35
2
12
8
67.
gx
Domain: all real numbers x except x 0
1 3x2 x3 x2 1
1
3 x x 3
x2 x2 Vertical asymptote:
Slant asymptote:
Line: y x 3
(b)
0
0 x 1
1 x
x 1
x 3
x 0
y x 3
69.
x 1
y
x 3
(a) x-intercept: 1, 0
0, 0 71. y
(a) x-intercepts: ±1, 0 (b)
1
x
x
65.
fx
Domain: all real numbers x except x 3
x2 5x 8
x 2
x 3
2
x 3
y-intercept:
Vertical asymptote:
Slant asymptote:
Line:
−14
8
0, 3
y x 2
8
−8
x 3
y x 2
10
−12
x 2 1
x ±1
12
−4
x 1
0
x
1
x
x
12