Section 10.1
G
raphing Squar
e Root Func
tio
ns
549
36.
ERROR ANAL
Y
SIS
Describe and correct the error in
comparing the graph of
g
(
x
)
1
—
4
√
—
x
to the graph of
f
(
x
)
√
—
x
.
2
2
x
1
y
f
(
x
)
x
g
(
x
)
x
1
4
The gr
aph of
g
is a horizontal
stretch by
a factor of 4 and a
re
e
ction in the
x
-axis of the
graph of
f
.
✗
In Exercises 37–
4
4, describe the transfo
rmations from
the graph of
f
(
x
)
=
√
—
x
to the graph of
h
. Then g
raph
h
.
(See Example 4.)
37
.
h
(
x
)
4
√
—
x
+
2
1
38.
h
(
x
)
1
—
2
√
—
x
6
+
3
39.
h
(
x
)
2
√
—
x
6
40.
h
(
x
)
√
—
x
3
2
41.
h
(
x
)
1
—
3
√
—
x
+
3
3
42.
h
(
x
)
2
√
—
x
1
+
4
43.
h
(
x
)
2
√
—
x
1
+
5
4
4.
h
(
x
)
5
√
—
x
+
2
1
45.
COMPA
RING FUNCTIONS
The model
S
(
d
)
√
—
30
df
represents the speed
S
(in miles per hour) of a va
n
before it skids to a stop, where
f
is the drag factor of
the road surface and
d
isthe length (in feet) of the
skid marks. The drag f
actor of Road Surface
A
is 0.75.
The graph sho
ws the speed of the v
an on
Road Surface B. Compare thespeeds by
nding a
nd
interpreting their av
erage rates of change o
ver the
interva
l
d
0 to
d
15.
(
See Example 5.)
46.
COMPA
RING FUNCTIONS
The velocity
v
(in meters
per second) of an object in motion is giv
en by
v
(
E
)
—
2
E
—
m
, where
E
is the kinetic energy of the
object (in joules) and
m
is the mass of the object (in
kilograms)
.
The mass of Object
A is 4 kilograms.
The
graph show
s the velocity of Object B. Compare the
v
elocities of the objects by
nding and interpreting
the ave
rage rates of change ov
er the interv
al
E
0
to
E
6.
0
2
0
1
2
3
4
468
E
Object B
Kinetic energy (joules)
Vel
ocity
(meters per second)
v
47.
OPEN-ENDED
Consider the graph of
y
√
—
x
.
a.
Write a function that is a vertical translation of
thegraph of
y
√
—
x
.
b.
Write a function that is a re
ection of the graph
of
y
√
—
x
.
48.
REASONING
Can the domain of a square root
function include negati
ve nu
mbers? Can the range
include negati
ve nu
mbers? Explain your reasoning.
49.
PROBLEM SOL
VING
The nozzle pressure of a
re
hose allow
s
re
ghter
s to control the amount of water
they spray on a
re. T
he
ow r
ate
f
(in gallons per
minute) can be modeled by the function
f
120
√
—
p
,
where
p
is the nozzle pressure (in pounds per square
inch).
(
See Example 6.)
a.
Use a graphing calculator to graph the function.
At what pressure does the
ow
rate exceed
300gallons per minute?
b.
What happens to the av
erage rate of change of
the
ow
rate as the pressure increases?
0
10
0
10
20
30
20
d
Road Surface B
30
Skid mark length
(feet)
Speed
(miles per hour)
S
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