556
Chapter 10
R
adical Func
tio
ns and Equatio
ns
34.
ERROR ANAL
Y
SIS
Describe and correct the error in
graphing the function
h
(
x
)
3
√
—
x
+
1.
x
y
22
2
✗
35.
COMPA
RING FUNCTIONS
The graph of cube root
function
q
is shown
. Compare the av
erage rate
of change of
q
to the av
erage rate of change of
f
(
x
)
3
3
√
—
x
over t
he interva
l
x
0 to
x
6.
(See Example 4.)
x
y
q
246
2
2
36.
COMPA
RING FUNCTIONS
The graphs of two cube
root functions are show
n. Compare the av
erage rates
of change of the two functions ov
er the interv
al
x
2 to
x
2.
x
g
h
y
2
42
4
3
2
37.
MODELING WITH
MA
THEMA
TICS
For a drag race
car that weighs 1600 kilograms, the velocity
v
(in
kilometers per hour) reached by the end of a drag race
can be modeled by the function
v
23.8
3
√
—
p
, where
p
is the car’
s po
wer (in horsepo
wer). Use a graphing
calculator to graph the function. Estimate the pow
er
of a 1600-kilogram car that reaches a velocity of
220kilometers per hour
.
(
See Example 5.)
38.
MODELING WITH
MA
THEMA
TICS
The radius
r
of a
sphere is giv
en by the function
r
3
—
3
—
4
π
V
, where
V
is
the volume of the sphere. Use a graphing calculator to
graph the function. Estimate the volume of a spherical
beach ball with a radius of 13 inches.
39.
MAKING AN ARGUMENT
Yo
ur friend says that all
cube root functions are odd functions. Is your friend
correct? Explain.
40.
HOW DO
Y
OU SEE IT?
The graph represents the
cube root function
f
(
x
)
3
√
—
x
.
x
y
2
42
4
2
2
f
a.
On what interva
l is
f
negativ
e? positi
ve?
b.
On what interva
l, if any
,
is
f
decreasing?
increasing?
c.
Does
f
have a
maximum or minimum va
lue?
Explain.
d.
Find the av
erage rate of change of
f
over t
he
interva
l
x
1 to
x
1.
41.
PROBLEM SOL
VING
Write a cube root function that
passes through the point (3, 4) and has an av
erage rate
of change of
1 over
the interva
l
x
5 to
x
2.
42.
THOUGHT PROVO
KING
Writ
e the cube root function
represented by the graph. Use a graphing calculator to
check your answer
.
x
y
24
2
2
3
Maintainin
g Mathematic
al Profi
ciency
Maintainin
g Mathematic
al Profi
ciency
Factor the po
lynomial.
(Section
7.6)
43.
3
x
2
+
12
x
36
44.
2
x
2
11
x
+
9
45.
4
x
2
+
7
x
15
Solve the equation using square
roots.
(Section
9.3)
46.
x
2
36
0
47.
5
x
2
+
20
0
48.
(
x
+
4)
2
81
49.
25(
x
2)
2
9
Reviewing what you learned in pre
vious grades and lessons
English
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