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Review for MAC 1140 Exam 3
1. (L14) Which of the following equations is ’odd’?
(a)
f
(
x
) =
2
x
±
1
(b)
f
(
x
) =
1
p
x
2
+ 5
(c)
f
(
x
) =
x
3
±
x
(d)
f
(
x
) =
j
x
j
(ans.
b
and
d
are even,
c
is odd).
2. (L14) Match the graph with its polynomial function,
y
=
(a) 2
x
3
±
3
x
+ 1
(b)
±
1
3
x
3
+
x
2
±
4
3
(c)
1
5
x
5
±
2
x
3
+
9
5
x
(d)
±
1
5
x
5
±
2
x
3
+
9
5
x
(ans. (c))
3. Given the graph below, is the degree of the polynomial even or odd? Is the leading coe±cient
a
n
positive or negative? Construct a possible polynomial that matches the graph and the given points.
(ans.
f
(
x
) =
x
2
(
x
+ 4)(
x
±
4), answer is not unique)
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View Full Document 4. (L14) Sketch
h
(
x
) =
±
1
3
x
(
x
±
4)
2
, determine the end behavior and intercepts, zeros, and multiplicities.
(ans. rises to the left, falls to the right;
x
±
intercept at
x
= 0(1)
;
4(2);
y
±
int
:
y
= 0)
5. (L14) Sketch
g
(
x
) =
±
5
x
2
±
x
3
, how many turning points does the graph have?
(ans. 2 turning points)
6. (L14) Find all zeros of
g
(
x
) = 2(
x
3
±
9
x
)(
x
+ 3)
3
(
x
2
+ 4)
3
and their multiplicities and determine if
graph touches or cross at the zeros; also ±nd the intercepts and end behavior.
(ans.zeros:
x
=
±
3(4)
touch;
0(1)
corss;
3(1)
cross
),
x
±
int:
x
=
±
3
;
0
;
3;
y
±
int:
y
= 0; end behavior:
rises on both sides.
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This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.
 Spring '08
 WILLIAMSON
 Calculus, Algebra

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