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Math 120 Final Examination Winter 2002
Your Name Your Signature
Student ID # Quiz Section
Professor’s Name TA’s Name
- Give all answers with 2 decimal point accuracy.
- This exam is closed book. You may use one two-sided 8
1
2
× 11
′′
sheet of notes.
- Graphing calculators are not allowed. Do not share calculators.
- You must show your work on all problems.
- To receive credit, you must write your final answer to each question in the box
provided.
- If you use a trial and error (or guess and check) method when an algebraic method is available,
you will not receive full credit.
- If you need more room, use the backs of the pages and indicate to the reader that you have
done so.
- Raise your hand if you have a question.
Problem Total Points Score
1 6
2 10
3 12
4 14
5 14
Problem Total Points Score
6 10
7 12
8 12
9 10
Total 100
- [6 points] Let f (x) =
3 + x
x
. Simplify
f (x + h) − f (x)
h
as much as possible.
- [12 points total] Let f (x) =
3 x − 2
2 x + 4
.
(a) [5 points] Graph y = f (x) on the axes below. Show the y-intercept, any zeroes, and
both horizontal and vertical asymptotes, if they occur.
− 5
5
− 5 5
(b) [3 points] Find the domain and range of f (x).
Answer:
(c) [4 points] Find f
− 1
(10).
- [14 points] Jody is riding a ferris
wheel of radius 45 feet. The highest
point on the ride is 95 feet above
the ground. The ride starts with
Jody at the point J; the wheel turns
clockwise at
3
4
RPM. Impose a
coordinate system as shown, with
the origin on the ground directly
below the center of the circle.
PSfrag replacements
J
(a) [4 points] Find Jody’s angular speed in radians per second.
Answer:
(b) [5 points] It takes 70 seconds for Jody to reach the top of the wheel. How far has she
traveled (along the arc) during these 70 seconds?
Answer:
(c) [5 points] Find Jody’s coordinates (x(t), y(t)) at time t seconds.
- [10 points total] Coffee is poured into a cup and left to cool. The temperature T of the
coffee (in degrees Celsius) is related to the time t (in minutes) since the cup was poured by
the equation
t = −25 ln
(
T − 20
75
)
.
(a) [3 points] When is the coffee 40
◦
C? (The answer should be the number of minutes
since the coffee was poured.)
Answer:
(b) [4 points] How hot was the coffee when it was poured?
Answer:
(c) [3 points] How hot is the coffee 10 minutes after it was poured?
- [12 points total] You are running a cliff-diving exhibition. Naturally, you are concerned
about the depth of the water beneath the cliffs. The depth at high tide is 25 feet; the
depth at low tide, which occurs three and a half hours later, is 5 feet. On one particular
day, you observe that at 6:30 AM, the depth of the water is 15 feet and falling. Here is a
graph of the depth of the water for the day in question, with t = 0 representing midnight.
6
(a) [4 points] Write the depth of the water as a sinusoidal model in terms of t, the hours
since midnight.
Answer:
(b) [4 points] How deep is the water at 1:00 AM?
Answer:
(c) [4 points] To dive safely, you require the water t be at least 10 feet deep. How many
hours during this 24-hour day will your divers be able to perform safely?
- [10 points total] Consider the multi-
part function f (x) defined on the
domain − 4 ≤ x ≤ 4 by the rule
f (x) =
2 −
1
2
x if − 4 ≤ x < − 2
3 +
√
4 − x
2
if − 2 ≤ x ≤ 2
5 − x if 2 < x ≤ 4.
(a) [4 points] On the axes to the
right, graph y = f (x).
(b) [4 points] On the axes below, graph y = f (
1
2
(x − 1)) − 3.
(c) [2 points] What is the largest domain on which y =
√
f (
1
2
(x − 1)) − 3 is defined?
