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Check Your Understanding
=
Step-by-Step Solutions begin on page R14.
Identify the domain and range of each function.
1.
f
(
x
)
=
√
4
x
2.
f
(
x
)
=
√
x
-
5
3.
f
(
x
)
=
√
x
+
8
-
2
Graph each function. State the domain and range.
4.
f
(
x
)
=
√
x
-
2
5.
f
(
x
)
=
3
√
x
-
1
6.
f
(
x
)
=
1
_
2
√
x
+
4
-
1
7.
f
(
x
)
= -
√
3
x
-
5
+
5
8.
OCEAN
The speed that a tsunami, or tidal wave, can travel is modeled by the equation
v
=
356
√
d
, where
v
is the speed in kilometers per hour and
d
is the average depth of
the water in kilometers. A tsunami in the ocean is found to be traveling at 145
kilometers per hour. What is the average depth of the water rounded to the nearest
hundredth of a kilometer?
Find the inverse of each function. Then graph the function and its inverse on the same
coordinate plane.
9.
f
(
x
)
=
3
x
2
,
x
≥
0
10.
f
(
x
)
=
x
2
+
2,
x
≥
0
11.
f
(
x
)
= -
6
x
2
,
x
≥
0
12.
f
(
x
)
=
1
_
2
x
2
,
x
≥
0
Practice and Problem Solving
Extra Practice is on page R5.
Identify the domain and range of each function.
13.
f
(
x
)
= -
√
2
x
+
2
14.
f
(
x
)
=
√
x
-
6
f
(
x
)
=
4
√
x
-
2
-
8
16.
f
(
x
)
=
√
x
+
2
+
5
17.
f
(
x
)
=
√
x
-
4
-
6
18.
f
(
x
)
= -
√
x
-
6
+
5
Graph each function. State the domain and range.
19.
f
(
x
)
=
√
6
x
20.
f
(
x
)
= -
√
5
x
21.
f
(
x
)
=
√
x
-
8
22.
f
(
x
)
=
√
x
+
1
23.
f
(
x
)
=
√
x
+
3
+
2
24.
f
(
x
)
=
√
x
-
4
-
10
25.
f
(
x
)
=
2
√
x
-
5
-
6
26.
f
(
x
)
=
3
_
4
√
x
+
12
+
3
27.
f
(
x
)
= -
1
_
5
√
x
-
1
-
4
28.
f
(
x
)
= -
3
√
x
+
7
+
9
29.
SKYDIVING
The approximate time
t
in seconds that it takes an object to fall a distance
of
d
feet is given by
t
=
√
d
_
16
. Suppose a parachutist falls 11 seconds before the
parachute opens. How far does the parachutist fall during this time?
30.
MODELING
The velocity of a roller coaster as it moves down a hill is
V
=
√
v
2
+ 64
h
, where
v
is the initial velocity in feet per second and
h
is the vertical
drop in feet. The designer wants the coaster to have a velocity of 90 feet per second
when it reaches the bottom of the hill.
a.
If the initial velocity of the coaster at the top of the hill is 10 feet per second, write
an equation that models the situation.
b.
How high should the designer make the hill?
Example 1
Example 2
Example 3
Example 4
Example 1
15
Example 2
Example 3
for a
Self-Check Quiz
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