B
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.
Name:
—
/ SQi~s
44~4LO*&
41i.d≤
Rational Functions
1. Completely factor the denominator of the rational function
—
2x2 + x
2z—5
—
2
Number:
_______
2. Find the vertical asymptotes of the graph of the rational function
_(z_4)(x+2)(x2+1)
@2
3. Find the x-intercepts of the rational function
+ 2)(x
—
2)
(z_4)(x+2)(x2+l)
—
(x2+2)(x—2)
~@ + 4)(z 2)
(z2 + 3x + 2)(x + l)~ That is, find and simplify the equa
tion 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 or intervals, using the correct notation.
5. What is the implied domain of f(x)
~
=
log2(x + 5)?
(-s,~)
6. What is the nnplied domain of g(z)
=
7. What is the implied domain of k(z)
=
3(x—1)(x--2)
—(x2 + 2x + 2)(x + 4)
_______________________
2~~?
Page 3
Translating: Logarithms ~ Exponentials
8. Write 1og10(12)
=
4z as an exponential equation.
ID
9. Write 1W
=
4x
=12.
x2 + 2 as a logarithmic equation.
=
Rewriting Logarithms
10. Rewrite 2 log6 (x)
—
3 log6 (y) as a single logarithm.
(xi
Page 4
11. Rewrite log12
1og12(z).
1o~ (~)
so that the
+
Ija
(~s)
only
-
logarithms that appear are 1og12(x), 1og12(y) and
~
(~)
(~) 31°~ ~ 1D~2 (%)
12. Rewrite 1og50(4) using logarithms with base a
13. What is the greatest integer less than log4(50)?
\~
(i~l
lO~q
(~4)z
3
Page 5
Solving Equations
14. Solve for x: 1og10(x + 1)
=
1og10(2x + 1) + 3
( )
jc~9x ~‘-777
.:
(0
3
)C+l
3
+10
~X
~÷ I
;oct& .{-IoDO
15. Solve for x: 10e2x
=
2e2x + 250
2S0
e
2TL
~~cv
S
/zcv
4
Page 6
Applications of Logarithms and Exponentials
16. A tree contained 1000 grams of carbon-14 when it died. If the amount of carbon-IA
decreases by ~ every year (that is, after one year, 20% of the carbon-14 is gone), how
much carhon-14 is left in the tree after t years?
)ooo(i
~)
loot
Algebra
17. Write
2
as a single power of a. (Your answer should look like a° where c C
0%
18. Eva’uate f(4) given that
f(x)— f~—2
1~x2~i~10
ifxe (—~,—4)
ifxc [—4,co)
Page 7
Graphs: Graph the following functions, and label all x- andy- intercepts, horizontal asymp
totes, and vertical asymptotes as indicated.
19. (4 points) Graph f(x)
4)~ Label any x- and y-intercepts, vertical
=
asymptotes and horizontal asymptotes.
20. (2 points) Graph h(x)
=
3~. Label any x- and y-intercepts.
21. (2 points) Graph g(x)
=
log2(z). Label any x- and y-intercepts.
22. (2 points) Graph k(x)
=
4~ + 1. Label any z- and y-intercepts.
23. (2 points) Graph 1(x)
=
—
1og10(x + 1). Label any x- and y-intercepts.
Page 8
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3.
Number:
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6.
7.
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13.
2-
14.
x=
16.
~.
10
)DOO
9.
I05~
ILl
c(~
(~+2)
17.
=
18.
•-997
}7fl
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L4zc
8.
a
a
15.
~
(~) -l ~ (~)
6k
c2(42
19. [(a:)
—13
A5u~my4o~re≤
~n4
~vfac~ s~a~p~9-
/
20. /i(x)
22. kG)
N
4
21. g(z)
23. 1(x)
0
:1-
~ pt
-fr
ce~ceJ
cLp÷ ~