576
Chapter 10
R
adical Func
tio
ns and Equations
10
10
Chapter Revi
ew
10.
1
Graphing Square Root Functions
(pp. 543–550)
a.
Describe the domain of
f
(
x
)
=
4
√
—
x
2
.
The radicand cannot be negati
ve. S
o,
x
+
2 is greater than or equal to 0.
x
+
2
≥
0
Write an inequality for the domain.
x
≥
2
S
ubtract 2 from each side.
T
he domain is the set of real numbers greater than or equal to
2.
b. G
raph
g
(
x
)
=
√
—
x
−
1. Describe the range. Compare the graph to the graph of
f
(
x
)
=
√
—
x
.
Step 1
U
se the domain of
g
,
x
≥
0, to mak
e a table of v
alues.
x
01
4
9
1
6
g
(
x
)
10
1
2
3
Step 2
P
lot the ordered pairs.
Step 3
D
raw a smooth curve
through
the points, starting at (0,
1).
T
he range of
g
is
y
≥
1. The graph of
g
is a translation 1 unit dow
n of the graph of
f
.
Graph the function. Describe the domain and range. Compare the graph to the graph of
f
(
x
)
=
√
—
x
.
1.
g
(
x
)
√
—
x
+
7
2.
h
(
x
)
√
—
x
6
3.
r
(
x
)
√
—
x
+
3
1
4.
Let
g
(
x
)
1
—
4
√
—
x
6
+
2. Describe the transformations from the graph of
f
(
x
)
√
—
x
to the graph
of
g
. Then graph
g
.
10.2
Graphing Cube Root Functions
(pp. 551–556)
Graph
g
(
x
)
=
−
3
√
—
x
−
2
.
Compare the graph to the graph of
f
(
x
)
=
3
√
—
x
.
Step 1
M
ake a table of va
lues.
x
61
2
3
1
0
g
(
x
)
210
1
2
Step 2
P
lot the ordered pairs.
Step 3
D
raw a smooth curve
through the points.
T
he graph of
g
is a translation 2 units right and a re
ection in the
x
-axis of the graph of
f
.
2
4
x
4
8
12
16
y
g
(
x
)
x
1
f
(
x
)
x
66
1
2
x
2
y
2
f
(
x
)
x
3
g
(
x
)
x
2
3
Dynamic Solutions
available at
BigIdeasMath.c
om
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