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Math 121
Spring ‘16
R. Mc Kenzie
Test 3
(4.1 – 5.6)
100 points
Name:________________________
March 25, 2016
Good Luck!
Please clear your desk of any unnecessary materials. This is a closed book, closed notes, closed neighbor exam.
Please write your answers where I can easily find them. Any scratch work you wish to have graded must be legible and
organized. The point value of each question is noted next to the problem number. You may leave when you have finished.
1.[12]
Let f ( x)  x  2 x  1 x  5
1a)
1b)
1c)
1d)
Find the leading term of f (x) .
Find the y-intercept of f (x) .
Find the roots of f (x) , and note their multiplicities.
Sketch a (very) rough graph of f (x) . Do not overly concern yourself with the scale of the axes.
2.[12]
Solve the following polynomial inequalities for x. Write your answers using interval notation.
You do NOT need to graph your results, but you might want to for your own sake.
2a)
2
x  22 x  13 x  5  0
3
2b)
x2 – 4x +1 < 0
x 2  4 x  2x  2
3
.

 1 2
2
x  1 x  1x  1
x 1
3.[14]
Let g ( x) 
3a)
3b)
3c)
Find any asymptotes of g (x ) .
Find any intercepts of g (x ) .
Sketch a graph of g (x ) on the axes below. Please use a 1-1 scale.
4.[12]
Solve the following rational inequalities for x. Write your answers using interval notation. You
do NOT need to graph your results, but you might want to for your own sake.
4a)
x4
0
x2
4b)
x4
1
x2
5.[24]
Solve the following logarithmic and exponential equations. You may round your answers to the
hundredths place.
5a)
log x  5  log x  5  2
5b)
log 2 x  5  log 2 x  5  3
5c)
5 x 3  30
5d)
4 x  2  5 x 1
6.[10]
6a)
6b)
Let P(x) = 2x4 + 5x3 + 6x2 + 10x + 4.
Use the Rational Root Theorem to determine the possible rational roots of P(x).
Factor P(x) completely over the Complex numbers.
Unnecessary bonus hint: 2i is a root.
7.[12]
Let f ( x) 
7a)
7b)
7c)
7d)
7e)
7f)
What is the domain of f (x) ?
What is the range of f (x) ?
Find f 1 ( x) .
What is the domain of f 1 ( x) ?
What is the range of f 1 ( x) ?
Show f f 1 ( x)  x .
8.[4]
Superman, Batman, or Wonder Woman?

1
.
x4
