Department of Mathematics
The City College of New York
Mathematics 19500
Final Examination
December 2005
Instructions: Show all work. Calculators are not permitted.
Please answer:
•
12 questions from Part I (5 points each)
•
5 questions from Part II (5 points each)
•
2 questions from Part III (7.5 points each).
Make sure to number each problem clearly in your answer book
Draw a box around each answer.
Cross out all scratch work.
Part I: Algebra and functions. Answer any 12 questions (5 points each)
1
.
Find equations of
a)
the vertical line through (2, 8)
and
b)
the horizontal line through (2, 8).
2.
Find an equation of the straight line through the point (3,7) that is parallel to the line
with equation
.
2
4
+
=
y
x
3.
Solve the inequality
12
5
1
≤
+
−
x
.
Write your answer in interval form.
4.
Solve the inequality
.
Write your answer using inequalities.
12
2
+
<
x
x
5.
Given
and
, find and simplify
.
2
3
6
7
)
(
x
x
x
f
−
−
=
x
x
g
−
=
2
)
(
))
(
(
x
g
f
6.
Given
3
)
(
+
=
x
x
x
f
, find the inverse function
.
)
(
1
x
f
−
7
. Given
, find and simplify
2
)
(
x
x
x
f
−
=
h
x
f
h
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 Spring '11
 Ocken
 Math, Trigonometry, Inverse function, Logarithm, exact value

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