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

21. C 70,000 120x 0.055x
The minimum cost occurs at the vertex of the parabola.
2 22.
0 0.107x2 26 0.107x
5.68x 74.5
2 5.68x 48.5
23.
26.
29.
31.
Vertex: b 120
1091 units
2a 20.055
Approximately 1091 units should be produced each day to
yield a minimum cost.
y x 3 , fx x 4 3 24.
−2
5
4
3
2
1
−3
−4
y
1 2 3 4 6 7
Transformation: Reflection in
the x-axis and a horizontal shift
four units to the right
f x 2x 24 y x4 ,
6
5
4
3
2
1
−3 −2 −1 1 2 3 4 5 6
−2
−3
y
is a shift to the right two
units and a vertical stretch of the
graph of y x4 f x
.
x
x
27.
f x 4x3 y x3 ,
3
2
1
y
−3 −2 −1
−1
−2
−3
1 2 3
x 23.7, 29.4
is a reflection in the x-axis
and a vertical stretch of the graph
of y x3 f x
.
y x 5 , fx x 3 5
−2
5
4
3
2
1
−5
1
3 4 5 6 7
Transformation: Horizontal shift
three units to the right
fx x 2 6x 9 30.
The degree is even and the leading coefficient is negative.
The graph falls to the left and falls to the right.
gx 3
4x 4 3x 2 2 32.
The degree is even and the leading coefficient is positive.
The graph rises to the left and rises to the right.
y
The age of the bride is
approximately 24 years
when the age of the groom
is 26 years.
Review Exercises for Chapter 2 241
x 5.68 ± 5.682 40.10774.5
20.107
x
x
25.
28.
−3
−2
Age of groom
27
26
25
24
23
22
y x 4 , fx 2 x 4
3
1
−1
−2
−3
y
y
20 21 22 23 24 25
Age of bride
1 2 3
Transformation: Reflection in
the x-axis and a vertical shift
two units upward
y x 5 ,
f x 1
2 x5 3
−6 −4 −2 2 4
8
6
4
y
is a vertical shrink and a
vertical shift three units upward
of the graph of y x5 f x
.
fx
The degree is odd and the leading coefficient is positive.
The graph falls to the left and rises to the right.
1
2x3 2x
hx x 5 7x 2 10x
The degree is odd and the leading coefficient is negative.
The graph rises to the left and falls to the right.
6
x
x
x