MATHEMATICS 111  PIECEWISEDEFINED FUNCTIONS
Problem #1.
Let
f
(
x
) =
3
x

1
if

5
≤
x <
1
4
if
1
≤
x
≤
3
6

x
if
3
< x
≤
5
.
(a) Evaluate
f
at
x
=

3
,
1
,
2
,
5
.
(b) On what interval is
f
constant?
(c) Sketch a graph of
f
. Is
f
continuous on its domain?
(d) Find the xvalue(s) where
f
(
x
) = 2
.
Problem #2.
Let
g
(
x
) =

2
x

6
if

8
≤
x
≤ 
2
x
if

2
< x <
2
1
2
x
+ 1
if
2
≤
x
≤
8
.
(a) Evaluate
g
at
x
=

8
,

2
,
2
,
and
8
.
(b) For what xvalues does
g
(
x
)
have a positive slope?
(c) Sketch a graph of
g
. Is
g
continuous on its domain?
(d) Find the xvalue(s) where
g
(
x
) = 0
.
Problem #3.
Let
h
(
x
) =

2
if
x <

2
0
if

2
≤
x <
0
3
x
if
0
≤
x
≤
4
.
(a) Determine the domain of
f
.
(b) Evaluate
f
(

2)
, f
(0)
,
and
f
(3)
.
(c) Graph
f
.
(d) Is
f
continuous on its domain?
Problem #4.
Let
f
(
x
) =
3
if

4
≤
x
≤ 
1
x

2
if

1
< x
≤
2
1
2
x
if
2
< x
.
(a) Determine the domain of
f
.
(b) Evaluate
f
(

2)
, f
(0)
,
and
f
(3)
.
(c) Graph
f
.
(d) Is
f
continuous on its domain?
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PIECEWISEDEFINED FUNCTIONS  MATHEMATICS 111
Problem #5.
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