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Part A: Multiple choice. Circle the correct answer. Sometimes more than one answer
is correct, and in those cases, circle all correct answers.
1. Find the domain of the piecewise-defined function,
f (x) =
(6 pts)
 2
x − 40



 x+5 , x<0



 x + 8,
x+1
a) all Reals
x≥0
b) ℜ, x 6= 0
c) ℜ, x 6= −1
Answer: d
Note: not continuous at x=0, but x=0 is defined
d) ℜ, x 6= −5
e) None of the above. The answer is:
2. If J.J. deposits $2500 is an account paying 6 14 % compounded monthly, what will the balance be in 30
months? Assume there are no other deposits or withdrawals.
(6 pts)
a) $2925.17
Answer: c
b) $2922.80
c) $2921.61
d) $2913.63
e) None of the above. The answer is:
1
3. Using completing the square, write in vertex form: f (x) = x2 − 2x + 11.
2
1
a) f (x) = (x + 2)2 + 9
2
1
b) f (x) = (x − 4)2 + 3
2
1
c) f (x) = (x − 2)2 + 9
2
1
d) f (x) = (x + 4)2 + 3
2
e) None of the above. The answer is:
4. Describe the end behavior of f (x) = ax4 − bx2 + cx + d if a, b, c and d < 0.
a) As x → ∞, y → ∞, and as x → −∞, y → ∞.
b) As x → ∞, y → ∞, and as x → −∞, y → −∞.
c) As x → ∞, y → −∞, and as x → −∞, y → ∞.
d) As x → ∞, y → −∞, and as x → −∞, y → −∞.
e) None of the above. The answer is:
(6 pts)
Answer: c
(6 pts)
Answer: d
a is defined in the problem as negative
Spring 2008
2
x2 − 9
4x2 + 6x − 11
,
g(x)
=
, and h(x) = log2 (x)
x2 − 2x − 3
2x2 + 1
1
lim f (x) + lim g(x) − h
x→∞
x→1
8
(6 pts)
5. Evaluate the following expression when f (x) =
a) 1
Answer: b
b) 7
c) 8
d) 2
e) None of the above. The answer is:
6. Write the equation of g(x) as related to f (x) shown below:
(6 pts)
a) g(x) = −f (x + 8) + 1
b) g(x) = −f (x − 8) + 1
c) g(x) = −f (x − 10) + 1
d) g(x) = −f (x + 10) + 1
Answer: a
g(x)
f(x)
2
e) None of the above. The answer is:
2
Part B: Work out problems. Show all necessary work, including any special features used on
your calculator. Box in your final answer.
7. Using the figure to the right of f (x),
answer each of the following questions.
(6 pts)
f(x)
a) Find lim f (x). 3
x→∞
b) Find
5
lim f (x). 3
x→−3−
c) Is f (x) a 1 − 1 function?no
2
d) Find lim f (x). DNE
x→1
e) Evaluate f (3) 2
−7
−3
3
5
7
f) What is the domain of f (x)? ℜ, x 6= −1
8. Find the intercepts, vertical asymptotes, horizontal asymptotes, and the x-value of any holes, if they exist.
3x2 − 11x + 10
(8 pts)
f (x) =
8 + 2x − x2
a) intercepts (0, 5/4),(2,0),(5/3,0)
b) vertical asymptotes x=4,x=-2
c) horizontal asymptotes y=-3
d) holes in the graph none
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9. Solve for x: log4 (2x + 1) + log4 (x − 3) = 1
(6 pts)
Answer x=3.5
The second possible answer x=-1, does not check.
10. Write the equation of the piece-wise defined function shown below, where each section is a transformation
of a linear function, quadratic function, square root function or an absolute value function.

, −5 < x < −3
 -x
2
−(x + 1) + 4.5 , -3 ≤ x ≤ 1
f (x) =
f(x)

| x − 3 | +2
,1<x
5
(6 pts)
2
−7
−3
1
3
5
7
11. Delta River Cruises rented a houseboat for $1200/month. Their cost for food and supplies for the four day
trip is $355/person. The rates they charge depend on the size of the group. If a family of five makes
reservations, they can cruise for $570/person. The Sullivans have 25 people getting together for a
reunion, and their fee is $550/person. Assume a linear relationship exist.
(6 pts)
a) What is the monthly cost function, if x = the number of passengers scheduled each month?
Answer: C = 1200 + 355x
b) What is the revenue function?
Answer: R = −x2 + 575x
c) Find the minimum and maximum number of passengers they should book each month in order to
make a profit.
Answer: [6, 214]
12. Solve for x: e2x + 2ex − 8 = 0 (Exact Answer )
(6 pts)
Answer: x = ln 2
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13. Given f (x) = x2 − 3x, find
f (2 + h) − f (2)
, and simplify completely.
h
(8 pts)
Answer: h + 1
14. Solve for x: 8x−2 = 3210−x
(6 pts)
Answer: x = 7
15. The table below gives Sabrina’s salary, in 1000s of dollars, since she began teaching in 1990.
Define t as the number of years since 1990.
Year
Salary
1991
24.9
1993
29.8
1996
33
2000
35.2
2005
37.1
a) Find the best fitting cubic, exponential, and logarithmic models and write an abbreviated version
below rounded to 3 decimal places. Then circle 1, 2, or 3 to indicate which model best predicts
her future salary.
(3 pts)
1. cubic
y1 = .009x3 − 0.289x2 + 3.281x + 22.017
2. exponential y2 = 26.490 ∗ (1.026)x
(3). logarithmic
y3 = 24.889 + 4.500 ln x
b) Using the unrounded regression model you chose in part (a) above, find her predicted salary for
2015.
Answer: $39, 374.01 (3 pts)
16. List the interval(s) over which each function below is continuous:
√
a) f (x) = 24 − 4x
b) g(x) =
x2 + 2x − 8
x2 + 6x − 16
(6 pts)
Answer: (−∞, 6)
Answer: (−∞, −8) ∪ (−8, 2) ∪ (2, ∞)