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

41.
fx xx 3 x 2 5x 3
(a) The degree is even and the leading coefficient is
positive. The graph rises to the left and rises to
the right.
(b) Zeros:
(c)
(d)
43. (a)
45. (a)
47.
3
(−3, 0)
−4 −2 −1
x 0, 1, 3
x 4 3 2 1 0 1 2 3
fx
100 0 18 8 0 0 10 72
−15
−18
−21
y
(1, 0)
1 2 3 4
(0, 0)
fx 3x 3 x 2 3
x 3 2 1 0 1 2 3
fx
87
25
(b) The zero is in the interval 1, 0.
Zero: x 0.900
fx x 4 5x 1
x
1
3 5 23 75
x 3 2 1 0 1 2 3
fx
95 25 5 1 5 5 65
(b) There are two zeros, one in the interval 1, 0 and
one in the interval 1, 2
Zeros: x 0.200, x 1.772
24x 2 16x
Thus, 24x2 x 8
3x 2
8x 5
3x 2 ) 24x 2 x 8
15x 8
15x 10
2
8x 5
2
3x 2 .
42. hx 3x2 x4 48.
4x 8
3x 2 ) 4x 7
4x 7 4
3x 2 3
29
33x 2
Review Exercises for Chapter 2 243
(a) The degree is even and the leading coefficient, 1,
is
negative. The graph falls to the left and falls to the right.
(b)
(c)
(d)
44. (a)
46. (a)
gx 3x 2 x 4
0 3x 2 x 4
0 x 2 3 x 2
The zeros are 0, 3, and 3.
x 2 1 0 1 2
hx
4
3
2
(( 3, 0 (( 3, 0
−
4
−4 −3 −1
−1
−2
−3
−4
y
4
3
3
29
3
(0, 0)
2 0 2 4
1 3 4
f x 0.25x 3 3.65x 6.12
x
fx
6
25.98
5
(b) The only zero is in the interval 5, 4.
It is x 4.479.
f x 7x 4 3x 3 8x 2 2
(b) There are zeros in the intervals 2, 1 and 1, 0.
They are x 1.211 and x 0.509.
x
6.88
4
3
2
4.72 10.32 11.42
x 1 0 1 2 3 4
fx
9.52 6.12 2.72 0.82 1.92 7.52
x 3 2 1 0 1 2
fx
416 58 2 2 4 106