Department of Mathematics
The City College of New York
Mathematics 19500
Final Examination
Spring 2006
Instructions:
Do 13 questions from Part I and 5 questions from Part II.
Show all work. Calculators are not permitted .
Part I.
Answer any 13 questions (5 points each)
1.
A parabola has equation
.
Find the coordinates of the parabola’s
intercepts and vertex and sketch its graph.
5
6
2
+
−
=
x
x
y
2.
Find an equation of the straight line through the point (4, 7) that is perpendicular to
the line with equation 2
x
+ 3
y
= 5 .
3.
Sketch the graph of
. Find all intercepts and asymptotes and label them
clearly on your graph.
3
2
+
=
−
x
e
y
4.
Solve the inequality
12
3
1
≤
−
x
.
Write your answer in interval form.
5.
Given
,
find and simplify
2
2
)
(
2
+
−
=
x
x
x
f
h
x
f
h
x
f
)
(
)
(
−
+
.
6.
Given
x
x
x
f
−
−
=
1
1
)
(
2
and
;
find and simplify
2
)
(
+
=
x
x
g
)
2
(
))
(
(
−
−
f
x
g
f
7.
Find the inverse of the function
x
x
x
f
−
−
=
1
3
2
)
(.
8.
The length of a rectangle is
x
. Its area is 50 square inches. Find a formula for its
perimeter in the form
______ .
=
)
(
x
f
9.
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 Spring '11
 Ocken
 Math, Derivative, Sin, Inverse function, Logarithm

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