77 / 84
Graph each function. State the domain and range.
31.
f
(
x
)
=
√
3
x
32.
f
(
x
)
= -
√
6
x
33.
f
(
x
)
=
√
x
-
7
34.
f
(
x
)
=
√
x
+
5
-
3
35.
f
(
x
)
=
3
_
4
√
x
-
1
+
5
36.
f
(
x
)
= -
1
_
3
√
x
+
4
-
1
37.
GEOMETRY
The area of a circle is given by the formula
A
= π
r
2
. What is the radius of a circle with an area of
300 square inches?
Example 4
Graph
f
(
x
)
=
√
x
+
1
-
2. State the domain and range.
Identify the domain.
x
+
1
≥
0
Write the radicand as greater than
or equal to 0.
x
≥ -
1
Subtract 1 from each side.
Make a table of values for
x
≥ -
1 and graph the function.
x
f
(
x
)
-
1
-
2
0
-
1
1
-
0.59
2
-
0.27
3
0
4 0.24
5 0.45
C07-063A-888482
O
x
f
(
x
)
The domain is
{
x
|
x
≥ -
1
}
, and the range is
{
f
(
x
)
|
f
(
x
)
≥ -
2
}
.
5-4
Graphing Square Root Functions
Graph each function.
38.
f
(
x
)
=
3
√
2
x
39.
f
(
x
)
=
3
√
-
4
x
40.
f
(
x
)
=
3
√
1
-
x
41.
f
(
x
)
=
2
-
3
√
x
42.
f
(
x
)
=
3
√
x
+
4
+
1
43.
f
(
x
)
=
2
3
√
x
-
1
+
2
44 .
GEOMETRY
The volume of a sphere is given by the
formula
V
=
4
_
3
π
r
3
. What is the radius of a sphere with a
volume of 400 cubic inches?
Example 5
Graph the function
f
(
x
)
=
3
√
x
-
2
+
1.
Make a table of values and graph the function.
x
f
(
x
)
-
5
-
0.91
-
4
-
0.82
-
3
-
0.71
-
2
-
0.59
-
1
-
0.44
0
-
0.26
1
0
2
1
3
2
4
2.26
5
2.44
C05_034A_903990
f
(
x
)
x
O
5-5
Graphing Cube Root Equations
connectED.mcgraw-hill.com363