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

133.
135.
fx 3x3 2x 2 3x 2
3x 2 x 4
x 1 23
, x 1
3 3x 4
(a) Domain: all real numbers x except
(b) x- intercepts: 1, 0 and
y-intercept:
(c) Vertical asymptote:
Slant asymptote: y x
(d)
1
x
3
4
3
x 3 2 0 1 2 3
y
((
C C
x
0, − 1
2
3x 2x 1x 1
3x 4x 1
3x 2x 1
3x 4
44
13
4
3
2
1
y
2
, 0
3
(1, 0)
−2 −1
2 3 4
−2
((
0, 1 2
12
5
1
2
2
, 0 3
x
0 2
x 1, x 4
3
14
5
134.
0.5x 500
, 0 < x 136.
x
Horizontal asymptote: C
As x increases, the average cost per unit approaches the
horizontal asymptote, C 0.5 $0.50.
0.5
0.5
1
Review Exercises for Chapter 2 255
fx 3x3 4x 2 12x 16
3x 2 5x 2
(a) Domain: all real x except x 2 or
(b) intercept:
intercepts: 4
, 0 , 2, 0
3 x-
y- 0, 8
(c) Vertical asymptote:
(d)
(a)
x 2x 23x 4
x 23x 1
x 23x 4
, x 2
3x 1
Using long division,
f x 3x2 10x 8
3x 1
Slant asymptote:
x
y
4
96
13
4
2
y
((
4
, 0
3
−6 −4 −2
4 6
−2 (2, 0)
−6
(0, −8)
1
21
4
x 1
3
y x 3
x 3
0 1 2 4
8
C 528p
, 0 ≤ p < 100
100 p
4000
0
0
x
1
2
0
x 1
3
5
3x 1 .
16
11
(b) When C million.
52825
p 25,
$176
100 25
100
When p 50, C million.
52850
$528
100 50
When p 75, C million.
(c) As p → 100, C → . No, it is not possible.
52875
$1584
100 75