MATH 1050-3: Exam 2
There are problems on both sides of each sheet.
March 13, 2008
Name:
U I.D:
Directions: To receive full credit, you must show all
of your work. Write your answer in the space provided.
Please box your answer and keep your work neat and
organized. You may not use a calculator, notes, or any
other electronic devices. If you need to use extra paper,
please label the exercises appropriately so I can find them.
If you finish early, take the time to check your answers.
Relax, enjoy, and no cheating! (Cheating is punishable
by a grade of 0%.)
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1. Write
3+2i
5+i
in standard form a + bi with a and b real numbers.
2. Use the properties of logarithms to expand the expression as a sum, difference, and/or
constant multiple of logarithms.
2 x
log5
y2z3
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3. Let f (x) = x3 − 3x2 − 4x + 12.
(a) List all the possible rational zeros of f (x).
(b) By checking the list, find at least one rational root. Use synthetic division to factor
the one rational root out.
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(c) Find the remaining zeros of f (x).
(d) Write the polynomial as a product of linear factors.
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4. Let
f (x) =
(x − 1)(x + 2)(x − 3)
x3 − 2x2 − 5x + 6
=
2
x + 5x + 4
(x + 1)(x + 4)
(a) Find the vertical asymptotes (if any).
(b) Find the horizontal asymptotes (if any).
(c) Find the slant asymptotes (if any).
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5. Find the exact value of log5 (75) − log5 (3).
6. Solve the following equation (Use the one-to-one property):
ln (x2 − 3x) = ln (3 − 5x)
Make sure you check your answer(s).
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7. (Extra Credit) Recall problem 4:
f (x) =
x3 − 2x2 − 5x + 6
(x − 1)(x + 2)(x − 3)
=
2
x + 5x + 4
(x + 1)(x + 4)
(a) Find all x- and y-intercepts.
(b) Solve for any additional solution points needed. For example, points on either side of
the vertical asymptotes and zeros are necessary.
(c) Draw a clearly labeled graph of the function using the information found here and in
problem 4. There is graph paper attached if you prefer to use it.
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