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

Section 2.2 Polynomial Functions of Higher Degree 155
21. ht
Degree: 2
2
3t2 5t 3 22. fs
Degree: 3
7
8 s3 5s2 7s 1
23.
25.
27.
29.
Leading coefficient:
2
3
The degree is even and the leading coefficient is
negative. The graph falls to the left and falls to the right.
fx 3x 3 9x 1; gx 3x 3 24.
8
−4 4
−8
−8
12
−20
g
g
f
f
fx x 4 4x 3 16x; gx x 4 26.
8
fx x 2 25 28. (a)
(a)
Zeros:
(b) Each zero has a multiplicity of 1 (odd multiplicity).
(c)
(a)
0 x 2 25 x 5x 5
Turning point: 1 (the vertex of the parabola)
−30
Zero:
x ±5
10
−30
(b) t 3 has a multiplicity of 2 (even multiplicity).
(c)
30
0 t 2 6t 9 t 3 2
Turning point: 1 (the vertex of the parabola)
−18
t 3
4
−20
18
Leading coefficient:
7
8
The degree is odd and the leading coefficient is negative.
The graph rises to the left and falls to the right.
fx 1
3 x 3 3x 2, gx 1
3 x 3
f
g
−9 9
6
−6
fx 3x 4 6x 2 , gx 3x 4
f
g
−6 6
5
−3
x ±7, both with multiplicity 1
(b) Multiplicity of x 7is
1.
(c)
fx 49 x 2
Multiplicity of x 7 is 1.
There is one turning point.
−30
0 7 x7 x
ht t 2 6t 9 30. (a) fx x2 10x 25
55
−5
30
x 5, with multiplicity 2
(b) The multiplicity of x 5 is 2.
(c)
There is one turning point.
−25
0 x 5 2
25
−5
15