Section 4.1
Piecewise-Defined Functions
347
Version: Fall 2007
4.1
Exercises
1.
Given the function defined by the
rule
f
(
x
) = 3
, evaluate
f
(
−
3)
,
f
(0)
and
f
(4)
, then sketch the graph of
f
.
2.
Given the function defined by the
rule
g
(
x
) = 2
, evaluate
g
(
−
2)
,
g
(0)
and
g
(4)
, then draw the draw the graph of
g
.
3.
Given the function defined by the
rule
h
(
x
) =
−
4
, evaluate
h
(
−
2)
,
h
(
a
)
,
and
h
(2
x
+3)
, then draw the graph of
h
.
4.
Given the function defined by the
rule
f
(
x
) =
−
2
, evaluate
f
(0)
,
f
(
b
)
, and
f
(5
−
4
x
)
, then draw the graph of
f
.
5.
The speed of an automobile travel-
ing on the highway is a function of time
and is described by the constant func-
tion
v
(
t
) = 30
, where
t
is measured in
hours and
v
is measured in miles per
hour. Draw the graph of
v
versus
t
. Be
sure to label each axis with the appro-
priate units.
Shade the area under the
graph of
v
over the time interval
[0
,
5]
hours. What is the area under the graph
of
v
over this time interval and what does
it represent?
6.
The speed of a skateboarder as she
travels down a slope is a function of time
and is described by the constant function
v
(
t
) = 8
, where
t
is measured in seconds
and
v
is measured in feet per second.
Draw the graph of
v
versus
t
.
Be sure
to label each axis with the appropriate
units. Shade the area under the graph of
v
over the time interval
[0
,
60]
seconds.
What is the area under the graph of
v
over this time interval and what does it
represent?
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1
7.
An unlicensed plumber charges 15
dollars for each hour of labor. Let’s de-
fine this rate as a function of time by
r
(
t
) = 15
, where
t
is measured in hours
and
r
is measured in dollars per hour.
Draw the graph of
r
versus
t
. Be sure to
label each axis with appropriate units.
Shade the area under the graph of
r
over
the time interval
[0
,
4]
hours.
What is
area under the graph of
r
over this time
interval and what does it represent?
8.
A carpenter charges a fixed rate for
each hour of labor.
Let’s describe this
rate as a function of time by
r
(
t
) = 25
,
where
t
is measured in hours and
r
is
measured in dollars per hour. Draw the
graph of
r
versus
t
. Be sure to label each
axis with appropriate units.
Shade the
area under the graph of
r
over the time
interval
[0
,
5]
hours. What is the area un-
der the graph of
r
over this time interval
and what does it represent?
9.
Given the function defined by the
rule
f
(
x
) =
0
,
if
x <
0
2
,
if
x
≥
0
,
evaluate
f
(
−
2)
,
f
(0)
, and
f
(3)
, then draw
the graph of
f
on a sheet of graph paper.
State the domain and range of
f
.
10.
Given the function defined by the
rule
f
(
x
) =
2
,
if
x <
0
0
,
if
x
≥
0
,
evaluate
f
(
−
2)
,
f
(0)
, and
f
(3)
, then draw
the graph of
f
on sheet of graph paper.
State the domain and range of
f
.