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

242 Chapter 2 Polynomial and Rational Functions
33.
35.
37.
39.
20
f x 2x2 11x 21 34.
0 2x 2 11x 21 −9
2x 3x 7
Zeros: x all of
multiplicity 1 (odd multiplicity)
Turning points: 1
3
2 , 7,
f t t 3
3 3t 36.
0 t 3 3t
0 tt 2 3
Zeros: t 0, ±3 all of
multiplicity 1 (odd multiplicity)
Turning points: 2
f x 12x 10
3 20x2 38.
0 12x 3 20x 2
0 4x 2 3x 5
Zeros: of multiplicity 2
(even multiplicity)
x of multiplicity 1
(odd multiplicity)
5
x 0
3
Turning points: 2
−5
fx x
(a) The degree is odd and the leading coefficient is
negative. The graph rises to the left and falls to
the right.
3 x2 2 40.
(b) Zero: x 1
(c)
(d)
x 3 2 1 0 1 2
fx
(−1, 0)
−4 −3 −2
−5
−5
−40
34 10 0 2 2 6
4
3
2
1
−3
−4
y
1 2 3 4
x
−3
5
9
4
fx xx 3 2
0 xx 3 2
Zeros: x 0 of multiplicity 1
(odd multiplicity)
x 3 of multiplicity 2
(even multiplicity)
Turning points: 2
f x x 3 8x 2
0 x 3 8x 2
0 x 2 x 8
Zeros: x 0 of multiplicity 2
(even multiplicity)
x 8 of multiplicity 1
(odd multiplicity)
Turning points: 2
gx x 4 x 3 2x 2
0 x 4 x 3 2x 2
0 x 2 x 2 x 2
x 2 x 1x 2
Zeros: x 0 of multiplicity 2 (even multiplicity)
x 1 of multiplicity 1 (odd multiplicity)
x 2 of multiplicity 1 (odd multiplicity)
Turning points: 3
(a) The degree is odd and the leading coefficient, 2, is
positive. The graph rises to the right and falls to the left.
(b)
0 x
The zeros are 0 and 2.
(c)
2 0 2x
x 2
2 0 2x
x 2
3 4x2 gx 2x3 4x2 gx 2x3 4x2 x 3
2 1 0 1
(d)
gx
18
(−2, 0) (0, 0)
4
3
2
−4 −3 −1
−1
−2
−3
−4
y
1 2 3 4
x
−10
−6
−4
0 2 0 6
3
−5
10
−80
3
−3
6
10
5