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

43.
45.
f x 2x2 5x 2
2x 2 x 6
(a) Domain: all real numbers except and
x 3
x x 2
2
(b) x- intercept:
(d)
f t t 2 1
t 1
(a) Domain: all real numbers t except t 1
(b) t- intercept: 1, 0
y-intercept:
0, 1
(c) Vertical asymptote: none
Horizontal asymptote: none
(d)
y-intercept:
(c) Vertical asymptote: x
Horizontal asymptote: y 1
3
2
x
y
2x 1x 2
2x 3x 2
−5 −4 −3 −2 1 2 3
, 0
1)0,
2 )
−
3 )
)
3
7
3
3
2
1
t 1t 1
t 1
−3 −2 −1 1 2 3
−1
−2
−3
(0, −1)
y
1
, 0 2
0, 1 3
4
3
2
1
2
5
y
(1, 0)
2x 1
, x 2
2x 3
1
3
x
t
0 1
1
3
1
5
t 1, t 1 46.
Section 2.6 Rational Functions 213
f x
(a) Domain: all real numbers x 4
x2 16 x 4x 4
x 4, x 4
x 4 x 4
(b) y- intercept: 0, 4
x-intercept:
4, 0
(c) Vertical asymptote: none
Horizontal asymptote: none
t 3 2 0 1
(d)
x 6 4 0 5
y 4 3 1 0
y 2 0 4 9
44.
f x 3x2 8x 4
2x 2 3x 2
(a) Domain: all real numbers x except x 2 or
(b) y- intercept: 0, 2
x-intercept:
(c) Vertical asymptote:
Horizontal asymptote: y
(d)
3
x
2
1
2
x
3 1 0
2
3
y
−4 −3 −2 −1 2 3 4
, 0
3
(−4, 0)
x 23x 2
x 22x 1
11
5
1
10
8
6
4
2
y
(0, 4)
−6 −2 2 4 6
−2
y
2
, 0 3
((
(0, −2)
3x 2
, x 2
2x 1
5 2 0 1
x
x
3
x 1
2