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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
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Chapter 2 Functions
Version: Fall 2007
9.
x
5
y
5
f
g
10.
x
5
y
5
f
g
11.
x
5
y
5
f
g
12.
x
5
y
5
f
g
In
Exercises 13

16
, 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, drop dashed, verti
cal lines through the points of inter
section, then label and shade the so
lution of
f
(
x
)
≥
g
(
x
) on the
x
axis.
Use setbuilder and interval notation
to describe your solution set.
ii. Make a second copy of the image on
graph paper, drop dashed, vertical lines
through the points of intersection, then
label and shade the solution of
f
(
x
)
<
g
(
x
) on the
x
axis. Use setbuilder
and interval notation to describe your
solution set.
Section 2.4 Solving Equations and Inequalities by Graphing
155
Version: Fall 2007
13.
x
5
y
5
f
g
14.
x
5
y
5
f
g
15.
x
5
y
5
f
g
16.
x
5
y
5
f
g
In
Exercises 17

20
, perform each of the
following tasks.
Remember to use a ruler
to draw all lines.
i. Load each side of the equation into
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