Math 1050
Exam 3
April 11, 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
answers on the answer sheet.
No cell phones, calculators, or notes are allowed during the exam. These
rules will be strictly enforced.
I
Name:
.
—
~rce~/
?~
Number:
Rational Functions
1. Completely factor the numerator of the rational function
—
2z2 + x
2x 5
—
roe
£
(x-t)
—
2
_________
2. Find the x-intercepts of the graph of the rational function
R ookc
0c
—
h\~AY’M~ro4or
3. Find the vertical asymptotes of the rational function
Rooks ~
_(z_4)(x+2)(x2+1)
(2 + 2)(x
2)
aenc~~~
(x2+2)(z—2)
2
—6(z 2)(x2 + 4)• That is, find and simp1i~ the equation
2(x2+2z+2))
of the function that the graph looks like to the far left and far right.
4. Calculate the end behavior of
—
3
Page 2
Implied Domain: Write you answers as sets, using the correct notation.
5. What is the implied domain of f(z)
6. What is tile implied domain of g(z)
=
1og10(—z)?
+ 3)?
=
R- h,’,
7. What is the implied domain of h(x)
=
4~?
R
Page 3
Translating: Logarithms ~ Exponentials
8. Write 1og10(x2 + 2)
tO
9. V/rite 104z
=
it
as an exponential equation.
x2~L
=
12 as a logarithmic equation.
q~
Rewriting Logarithms
10.
Rewrite log3(x) + 3 log6(y) as a single logarithm.
\ojJx) f
lo~(j3)
Page 4
11. Rewrite 1og12(xy3z) so that the only logarithms that appear are 1og12(x), 1og12(y) and
1og12(z).
(~)
(~)
(~)
(j)4
12. Rewrite log4 (50) using logarithms with base e.
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13. What is the greatest integer less than 1og10(4999)?
(iooo~
I 05~~ /ioUoo)
3<
Page 5
\05;t
Solving Equations
14. Solveforz: log3(x+2)—log3(z—1)—2=O
/ ~÷z
O5~ ~zr
x+Z
K
15. Solve for z: 22x_1
—
5
=
11
Zr-’
H
Lb Zx-
I
Page 6
Applications of Logarithms and Exponentials
16. A tree contained 5000 grams of carbon-14 when it died. If the amount of carbon-14
decreases by ~ every year (that is, after one year, 10% of the carbon.-14 is gone), how
much carbon-14 is left in the tree after t years?
Algebra
17. Write
(4)3 as a single power of a.
=
6k
{çO}
18. Evaluate
f(—4)
(Your answer should look like aC where c e R.)
given that
I
~—2
f(x)= ~x2+1o
Y (-4)
if
xE (—~,—4)
ifxe
[—4,~)
I~
Page 7
Graphs: Graph the following functions, and label all x- andy- intercepts, horizontal asyrnp
totes, and vertical asymptotes as indicated.
19. (4 points) Graph f(z)
=
~+i)~~• Label any x- and y-intercepts, vertical
asymptotes and horizontal asymptotes.
20. (2 points) Graph h(x)
=
21. (2 points) Graph g(z)
=
22. (2 points) Graph k(z)
=
23. (2 points) Graph 1(x)
=
log4(z). Label any x- and y-intercepts.
(W.
Label any x- and y-intercepts.
~(3~). Label any x- and y-intercepts.
2log10(x + 10). Label any x- and y-intercepts.
Page 8
Number:
L
‘3
3.
4.
5.
31e6.
7.
)(~~ 4- 0
(tt -2
‘1,
10.
1
1
11.
13.
o)
14.
~o,l3~
15.
\~-
8.
10
9.
to~ip
16.
77~
(~)~
17.
Lf~
correth
Sc4
In~ (~)~3
[m(1r)
12.
-3~
~-
2(~
Io~a(~~”
x=2
(-~,
Q~,
18.
no+cik~pn.
3
xt
Y~
::
II /
Is’
)
y-b
eocht
19. f(.r)
• Asjrn.94~-t-es
• End EeV~ovior
•
I
20. li(x)
22. k(x)
21. g(x)
23. 1(x)
-.
t2~ —2-3
I Vt
coY1’~~
4~Tv jvvhrctF+S
Skc4&/
IU-~
ontfl~1 Ufl
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