Math 110
Final Exam
All Sections including SL Center
April 16–17, 19–21, 2010
1. What is the range of the function defined by the equation
y
=

x
2
+ 6
x
+ 3?
(a) (
∞
,
3]
(b) (
∞
,
6]
(c) (
∞
,
9]
(d) (
∞
,
12]
(e) (
∞
,
15]
(f) (
∞
,
18]
2. If
b
and
c
are real numbers so that the polynomial
x
2
+
bx
+
c
has 3 + 2
i
as a zero, find
b
+
c
.
3. Let
R
(
x
) =
3
x
2
+ 5
x
+ 1
x
+ 2
. Then
R
(
x
) has an oblique asymptote at:
4. Solve the inequality:
x
(
x
2
+ 2
x
+ 1)
x
2

4
x
+ 4
≤
0
5. Solve the inequality:
5
x
+ 1
x
≥
6.
(a) (
∞
,
1]
(b) (
∞
,
1)
(c) (

1
,
0)
(d) [

1
,
0)
(e) (0
,
1]
(f) (0
,
1)
6. Find
k
so that (
x
+ 3) is a factor of
x
100

9
x
98
+
kx
2

5
x
+ 3.
7. Using the fact that

2 and
1
3
are zeros of the polynomial,
f
(
x
) = 3
x
4
+ 5
x
3
+
x
2
+ 5
x

2,
find the sum of the other two zeros.
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 Fall '08
 Staff
 Real Numbers, Conic section

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