Chapter 10
Chapter
R
eview
577
Graph the function. Compare the graph to the graph of
f
(
x
)
3
√
—
x
.
5.
g
(
x
)
3
√
—
x
+
4
6.
h
(
x
)
8
3
√
—
x
7.
s
(
x
)
3
√
—
2(
x
3)
8.
Let
g
(
x
)
3
3
√
—
x
+
2
1. Describe the transformations from
the graph of
f
(
x
)
3
√
—
x
to the graph of
g
. Then graph
g
.
9.
The graph of cube root function
r
is show
n.
Compare the av
erage rate of change of
r
to
the ave
rage rate of change of
p
(
x
)
3
—
1
—
2
x
over th
e interva
l
x
0 to
x
8.
10.3
Solving Radical Equations
(pp. 559
–566)
Solve
√
—
10
−
3
x
=
x.
√
—
10
3
x
x
Write the equation.
(
√
—
10
3
x
)
2
x
2
S
quare each side of the equation.
10
3
x
x
2
Simplify
.
0
x
2
+
3
x
10
S
ubtract 10 and add 3
x
to each side.
0
(
x
2)(
x
+
5)
F
actor
.
x
2
0 or
x
+
5
0
Zero-Product
Property
x
2 or
x
5
Solve
for
x
.
Check
Check each solution in the original equation.
√
—
10
3(
2
)
?
2
Substitute for
x
.
√
—
10
3(
5
)
?
5
√
—
4
?
2
Simplify
.
√
—
25
?
5
2
2
✓
Simplify
.
5
≠
5
✗
Because
x
5 does not satisfy the original equation, it is an extraneous solution.
The only solution is
x
2.
Solve the equation. Check yo
ur solution(s).
1
0.
8
+
√
—
x
18
11.
3
√
—
x
1
3
12.
√
—
5
x
9
√
—
4
x
1
3.
x
√
—
3
x
+
4
14.
8
√
—
x
5
+
34
58
15.
√
—
5
x
+
6
5
1
6.
The radius
r
of a cylinder is represented by the function
r
—
V
—
π
h
, where
V
is the volume and
h
is the height of
the cylinder
.
What
is the volume of the c
ylindrical can?
2468
x
y
r
2
4
6
4 in.
2 in.
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