Section 2.4
Solving Equations and Inequalities by Graphing
153
Version: Fall 2007
2.4
Exercises
In
Exercises 1

6
, you are given the de
finition of two functions
f
and
g
. Com
pare the functions, as in Example 1 of
the narrative, at the given values of
x
.
1.
f
(
x
) =
x
+2
,
g
(
x
) = 4
−
x
at
x
=
−
3
,
1, and 2.
2.
f
(
x
) = 2
x
−
3
,
g
(
x
) = 3
−
x
at
x
=
−
4
, 2, and 5.
3.
f
(
x
) = 3
−
x
,
g
(
x
) =
x
+9
at
x
=
−
4
,
−
3
, and
−
2
.
4.
f
(
x
) =
x
2
,
g
(
x
) = 4
x
+ 5
at
x
=
−
2
,
1
, and
6
.
5.
f
(
x
) =
x
2
,
g
(
x
) =
−
3
x
−
2
at
x
=
−
3
,
−
1
, and
0
.
6.
f
(
x
) =

x

,
g
(
x
) = 4
−
x
at
x
= 1
,
2
,
and
3
.
In
Exercises 7

12
, perform each of the
following tasks.
Remember to use a ruler
to draw all lines.
i.
Make an accurate copy of the image
on graph paper (label each equation,
label and scale each axis), drop a dashed
vertical line through the point of in
tersection, then label and shade the
solution of
f
(
x
) =
g
(
x
)
on the
x
axis.
ii.
Make a second copy of the image on
graph paper, drop a dashed, vertical
line through the point of intersection,
then label and shade the solution of
f
(
x
)
> g
(
x
)
on the
x
axis. Use set
builder and interval notation to de
scribe your solution set.
iii. Make a third copy of the image on
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1
graph paper, drop a dashed, vertical
line through the point of intersection,
then label and shade the solution of
f
(
x
)
< g
(
x
)
on the
x
axis. Use set
builder and interval notation to de
scribe your solution set.
7.
x
5
y
5
f
g
8.
x
5
y
5
f
g