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MAC1140, Precalculus Algebra, Summer B 2007
Review Problems for Exam 4
1. Find the average rate of change of
f
(
x
) =
x
3

x
over the interval [

3
,
1].
2. For the function
f
(
x
) =
3
 
x
+ 3

if
x
≤ 
1
1
if

1
< x
≤
1

x

3
 
1 if 1
< x .
ﬁnd all the (open) intervals where the function is decreasing, increasing
and constant. Also ﬁnd any local maximum and minimum.
3. Sketch all intermediate steps that are needed to graph the function
(translating, ﬂipping, stretching) starting from the basic function.
a)
f
(
x
) = 2(
x
+ 2)
2
+ 1
b)
f
(
x
) = 1

1
2

x

c)
f
(
x
) = 2 +
√

x
4. Sketch a graph of the following functions (ﬁnd vertex and all inter
cepts):
a)
f
(
x
) = 2(
x
+1)
2

3
b)
f
(
x
) =

2
x
2
+8
x

8
c)
f
(
x
) =
x
2

x

6
5. What are the ranges of the following functions:
a)
f
(
x
) = (
x

2)
2
+ 1
b)
f
(
x
) =

2
x
2
+ 8
x
c)
f
(
x
) = 5

3
√
x
+ 2
6. A ball is thrown upward with initial velocity 80 feet per second and
from a tower of height 96 feet.
a) Find an expression for the height
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This note was uploaded on 06/09/2011 for the course MAC 1140 taught by Professor Williamson during the Summer '08 term at University of Florida.
 Summer '08
 WILLIAMSON
 Calculus, Algebra, Rate Of Change

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