Name c(,'Q IIAtianS
May 6, 2010
Show all work on exam. Non-graphing calculators allowed. Closed book and notes. This exam is worth 100
points. Do well!
Math 29, Section 3 1. (15 pts) Graph on the same coordinate system. Label each graph with the equation it represents.
a. [(x) = 3 x
b. [(x) = -3 x + 1
c. [ex) = 10g3x
-~
lj:::' ...-v'V'-)
PI V l 3 X
-\
3'1 ~ X.
o
1 .
I
~-
'J-.
r
0
3
I
113
-\
<1 J.
Yq
-J :z...
-)...
-'6
-q
3
-3~
X
-~
-\
-t \
'21 q
'2../ 3
0
0
\
.- J..
a -8
2. (15 pts) SimplifY.
i a. log 10 3x :::-?:>)l
I b. e 1n(x-l) :::. 'X _\
I c. log]!! .:::::- 0
( d. logbb 3 -:::.. 3
( e. JogFss ;::
a
4 -V2­
,
=
4-l/-:z­
-
\
--1
YIt-:L
g. Write in logarithmic form: 4 x = 16
.J\ h. Condense and simplifY: log(a 2 b) -log(2a)+log(b)
!oj
~
1.
J.;-'2CL T
n;J..
~j.
()
)(r
9-0~ ~ -t iHJ~p \
to (¥}/r) c=:~)
J
What is the domain of I(x) =~Og(X _ 4)?
.
~"-4 >D
eX -2.,") (x -t"L)
X:::·')..
D i~
T~
>0
X:::.. - J..
+-1~
f;;~
~~------r\------~----
o
1-.::'-0:
D~~-Y:
;60
3. (20 pts) Solve for the unknown variable.
a. S3X 2­
25
s~)(.
-: : .
~5-' 5~)(
:::
(5'2.)-1 S-d. .:;>
1'5"'>1- ;::
b. log4(2x - 3) = 2
ttl. :::
2...,.. - "3
\lP-=-2-y..-3
III
=-
'2-)<.
[g. =- x]
...eDS:l )( CY-. -1') -:: 3
;)3
g
=- X (X - '1)
::=. X"l--~X
D::: ')('"}--1x-<g
d. 2logx - log 7 = log 3
Qo~ Xl. -1.1)5 1 =- I~ 3 .9-05 (¥j
::=
Wj
'f...?-'
-"1 =-3
:x?' = :+-\ 3
()<.-'3)(¥.
-t-\):::D
J 'f:.-=-~) ~~
4. (20 pts) Answer the short questions. Do NOT use a calculator, except on part (g). Leave radicals, do
NOT convert to decimal.
. (
25 )
a. sm
- '31l'
=~ (-1) \
1J
=[
b~ sec (»;:: ~ ( 10 ~ 1T)
= SU:.
(
-Q -rr) ;:::. ~ (<:D~ )
:= JJ/f
~c.
~ =- ~ @)(
casC -~):c
f'-:. \
t!'-'11­
(01- 1)
2­
!:;: ~
\
@
. ---f----'-.......
d. If sin (J = ::, use right triangle trigonometry to find an expression for tan (J.
2
~
~+)(
..
y"''=
")...
=-d­
")...
"2... ;l - X
l1::.
'l..
....
:: 4 -x "­
tl ~ -xl.. e. Use trigonometric identities to find the exact value:
2 1
sec (90°-0)
+ cos 2 (J
f. Simplify
this expression so that it only involves one trigonometric function:
.
\
tan
2 9~' 120
Sill
\!
~ee- =- J~l- t3- ~
g. Find e for the right triangle shown below. (OK to use calculator.) (LASe 10..0\ IO-t"\5
+COS
II
1.
)
29)
5. (15 pts) Graph one period ofy = 2 cos(4x - :!:). Label the values of the five key points on the x-axis.
2
State the amplitude, period and phase shift.
(5"YL(
~de
o ~ 'i
A-l c:; ;}..:n
'1.l.,L.,
C)..
-lfx
6.
Leave radicals in answers, do not convert to decimal.
~<o
X=- -3 I
-
S-uv\ 9-
-\
=- ---Vl{) -=
~e-::
-ftO
­
10
-3m
v
,V
-3
<:..-sce :: -- 110
~e-=-~
3
H)
to...t., e--=
y-.:::. f)(")..t,,~?
:: 1C-3 )1--\- {-l)"l.
:: --( q
't" \
:::
{TO
.L
3
coie =-3