Math
1050
Practice Exam 3
April 6, 2012
Answer all questions below. Every question is worth the same number of
points. You may use the available space for work, but must write ALL
~mswers on the answer sheet.
No cell phones, calculators, or notes are allowed during the exam. These
rules will be strictly enforced.
Name: _______________________________________________________ Number:
~ ~••(
Rational Functions:
1. (2 points) Completely factor the numerator and the denominator of the rational function
x3_3x2+2x_6
(x-3)~~
3x—3
2. Find the zeros for the rational function 3~
Kt’,
1)(x
x+2
—
—
3)~
?c:
3. Find the vertical asymptotes of the rational function 3@
(x
4. Calculate the end behavior of
2 (x
X
2
—
-
1)(x + 2)
4)(x + 5)
Implied Domain:
5. What is the implied domain of f(x)
=
1og19(x)?
Y>o
6. What is the implied domain of ~
7. What is the implied domain of h(x)
=
=
(x + 5)7
x(x
—
4)
4z7
Translating: Logarithms ~ Exponentials:
8. Write log4(x + 1)
=
as an exponential equation.
Vt
9. Write ir3Z2
=
42 as a logarithmic equation.
~
(~
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Rewriting Logarithms
10. Rewrite log6(z)
—
log6(y) + log5(z) as a single logarithm.
)
Lo~(
11. Rewrite log12(~’) as the sum and difference of several more basic logarithms.
-
12. Rewrite log4(x) using logarithms with base 10.
Lo~~~0
(‘1)
13. What is the integer part of log10(1025)?
Solving Equations
14. Solve for x: log9(lOz)
—
log2(x
—
1)
=
14
iq
Lo a!
~ x-I}
laY
2
__
2~’ ~
lo)<
15. Solveforx: et+7=3ex
,<( a”1_1a)
Page3
‘9
/9
q
Application
16. Suppose you accidentally open a canister of plutonium in your living room and 256 units
of radiation leaks out. If every year, there is half as much radiation as there was the
year before, how many units of radiation will there be after t years?
5~
(j)t
Algebra
17. Write
as a single power of a.
18. Evaluate f(4) given that f(x)
=
{
~+1
Page 4
~
Graphs
19. (4 points) Graph f(x)
=
3(x—3)(z+2)
Label all important information.
xG+4)
20. (2 points) Graph li(x)
=
4X•
21. (2 points) Graph g(x)
=
log4(x). Label any x-intercepts. Label any y-intercepts.
22. (2 points) Graph k(z)
=
23. (2 point
Graph 1(x)
.
.
Label any x-intercepts. Label any y-intercepts.
+ 4. Label any x-intercepts. Label any y-intereepts.
=
—
1). Label any x-intercepts. Label any y-intercepts.
~q.
0
‘go.
1-.
/
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