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Math 35 Final Exam
Name:
C1re.c\1A
So.\ c\Cb,na.
Be sure to show all of your work clearly on each problem. Unjustified answers may result
In reduced credit. Box answers when possible.
Simplify each of the following expressions completely (problems 1- 4):
I.
2.
J 144xtoy•
J 3xy 2
5 '2..
I')
t :,L. )(, ::..J..L
~
)',_
--
j ·~x
"8
\ 2. )<. .S'
~~x"'
::- \2.. XS
-
I
•.
v?~
J
-
-
l; ~ Y
.- 1--·-7
:; -'JJ
t, ~-~
J
l\ 1, '.)- 3x"l. +- b:t -\ .5
x+-~ l '-\x'-i+sx3 +0)(.-z.-3x-\
-L, Atl _
l
- 3 )(.?i -r o.X.:- '3 - ,
-t3x~+~~
-
b? -3~-\
"'-'11:'l -\?,)(
-IS,<-\
+ 1sx
tao _
9..
Solve each of the following equations (problems S-10): (Give ALL real/complex solutions and
check answers when appropriate.)
5.
3x
4
Sr
l
15x 3
-
+ 12x 2 - 60x = O
(x':>-5)(-\-'i >-.-~~= o
--1.?- ( Y-. - 5'}:..C L\ ( '1--- ~
::>X (..,,._-i .\ ~()( · 5) :: o
)(.-5:: 0
-r S 4 5
l!~J
~+1=~
x 2 -2S
x+s
6.
l oo
y.?--:J.
-._i"L-,
" y...
'
-t- X?. - l~ _
l ')
illll" -
c. .
+- \ 2 -2~, t...7- ( x.-S)
_j
1(--;,'Lz) :. X-\"5 (:x.--s)
,
~~-l~{
y...~-~5
\ C)O -\ y._o..-~5
- \ :)0 -
1 _._.-,
)(
=:;,_ ,/·- .../1
c
_ , _,1.._.J
0
~~-is )
-
\
(s___,
-\ \ S
J- ::_ ,5 j
\O)(
- \0i)".lt-1S
!:- -----"'- -y._"l...- 10)(. - 7S
o :: (-;.__ )(- \':)::.o
'2._
,si_ 'f... "T SJ
7.
..Jx+ 10- ~ = 4
~ ,,.:.
-I )(
1...-
- - · l.
)'- -\ \ v)-:.. Ci- """I..\ )
X~ \a ::.. ').."2. +~~~ \ 1.?
- 10
"l.
;,:_-:.. '/,.. k~)'-...,..0
- '\o
- 7-~
o-: 'i-7.. -1-1~"'f'lo
=C ~-r~ c~~~
C,Y\Ll'< '
~ ( ) -(.-~) -: <- \
+~ -: L.\
-
+ b -::- ~1
I- L.\
I, -\ -\- \ ~
fq
-
(- \) :, Lj
-+\ --: L..\
?;-t\·L\
l \ :.. t...\
8.
32x+s
27
Jl, )(.1"
5
.9,.)( 1
-5
3
8
= .!..
I
::3
::J
- '3
:: 3
~-,("t ~ :: -3
-1'5
-5
¥ ~-;
) 'f.. -:. - L\ \
9,
=2
log.x + log 4 (x - 15)
l n~ '1 i- (y,_- \S; -=-,, 'J..
'<..
X(
\ SJ=- L\
X (_ )(- ,<:,) .: l\o
x-
X..,_ _ \ ':)~ =-
-
l6
- \1o - \1,, x'l. -
1 s)(.- \ 1o:. o
l. v,
x - , b=-o
w (.,\ h ) ...- wvi
+ 3) 2 - 4(x + 3) + 3 = O
(lt 0x ~<"1)
X
'2
- L\ '/.....,. 1i
q - L\
...,
)( - -\ 1.)(.::_ D
><(x~'"LJ :::.. o
)(kl:::.
o
-l
..:::::.--
-2.
)( -:. - l.
)(.. ::: 0
I
+3-=o
- 11 -\
'I- -;, -;l.
L\
' t.i
\,V'-0.>-tr ...,_,,~
X=- I\..
(x
"c)l-\
<tL.\
--1\lo'\\L,,
l 0.
h 1 -. w is (-1 - 10-::: 2
(._ )( - \ ~{-,z +'1 -:: C>
3 -=
0
( - 1t,l:. 1..
Solve each of the following lnequalltles and write your answer In Interval notation (problems 11 •
12). Make sure to show your work for each problem, lndudlng sign charts when approprtate.
11 .
-212x - 11 + 13
-,4. -3 ;.
- J_ ~
)(
=-~./
;>
-;z
- :2.
\g_-,(_ -\\ ~ 5
i~- ,
- 5
4 \
- \
- '-\
.Q
;;;.
L.
5
._,
(p
'I-
:2
X ~3
-...,,. .
3
12.
x 2 +4x+3
x-5
::5
(;,<_-\'~)) ( / \
O
)<.A-\=O
I
- I
- I
)( -=-- \
j
- \
¢ ~ -+- . +- I \
\ \
I -I
( - (J:),· ~/ (· :,,~I 0 ( - i , ?)
X -r l
)( - 5
6
i ( :S7I00)
Graph each of the following and give the requested Information for each. Please make sure to
label your axes and show your scale. (Problems 13-18)
13 .
g(x)=-lx-41+1
·- \
£. I 1 _. \
f
-
!
I
..1
I - •\
..1
I
-
}
/
/
-~
· 1·
'
/
-
/
-
I~
/
,
'f
I
~- - \
I~_,
- \ - ,,\ .l. \
- - L\ - \
'!_; : - 3
/'
C
/
I
·'\,..1\
(
V
', I -
'
. J
"I- - -
-
'I -_ '-- ,
-
\
b
t
14. For problem 13, give the following information:
ls it a function? - - '--.'-=.-:. C
. :. .1:_ _ __
-
Domain: _ _.:..
( -- --'l'---);-c-{)._j
):.)
~
,
-
I <
1 - -,--...
x-intercept(s ): ---''C.0:'-''-------''- --l~•~
' i~ - -
Is it one-to-one? ~ ~,
- ----Range: - --~ -~ -- - - - - y-intercept(s):_ _ _~ ~ -- -
.\
Y = x2
15 ·
-
1vf
0-'
4x + 2
\l
, .J
('
\
\
'T
\
\
'
I
'
'
µ
)
\
'
"'
'
I
'
,/
v \ 1,U, - ~'.l._
-' \
I
.. 'f
I
'"\
I
l-\
1
s
"1
~-
-,
-
-1
-\
J
- \"_...
\ l
- ::,~
1- 1
r
'
, } - (\ ( ",)
I
I
J
/
-
,.,
0
'l
y, ,
-1 r
-::i
- \
/
·,
1..
'\
\.
-1, I'
') _. -~
- ,,., "
'\
'J
16. For problem 15, give the following information:
Standard/Graphing Form ofthe Equation:
\
,, _.,____ _ _ _ _ _ _ _ __
.........,_
_ __,_____c."'_
Is it a function? _ _..c,l)!'-',e='>
. _ _ __
0omam:
-- sJ ,
M
x-intercept(s): __'-:.....:..:c;:_~~ J?
...:..1...,.1....:cOJ
...,____ _
C) -_
- (- , ,, :
:;,
(
\l : ~
Is it one-to-one? - Iv O ---Range:
'l }
( lJ
1_
•\
:.
\ lo - 'i
I
0)
y-intercept(s ):_ . .(_o+o_ 1-:i.._
;),____ __
:) -_ 1..
- ,(
C.- ::i.
-_ 'o'L -'-\ ( u· 1 'I l
"
-r-'-j
'I .\- '.l..
C.
l•r- l )' -~ - -'.l.
/2.J
17.
Y
, I'
== log 2 (x - 3) + 2
)
,
'
....;
-
I
l/
/
i....-
f
I
7
r,,
\
I
1
;
(
)
""
•
18. For problem 17, give the fo llowing informaLion:
Is it a function? - -=
' _,_J____
:i , kl
Domain:
x-intercept(s) :
I")-
))
Range:
1
0
-~----'L-'\ -'1_ ....__ _ __
!,1
____
Is it one-to-one? ---'-_.,_
v)'
( - 0 , ,._,
y-intercept(s):_ .r._2
'-'-'-f\J___ _ __ _
( I '.11~ '2..
'
= x2 -
2x and g(x)
= 3x -
+ g)(x).
:: t (i',.
o,. ( xJ
19. Given that f(x)
a)
(f
5, fiQd each of the following:
-- c'/..."L-1-:;1 l. c::. ~- ">J
- 'i-. '2_ '1 )(.. ..\ ?, ')<_ -
,- ,,- -
---
.5
'/--.--+ j-..- 'j
b)
(f- g)(x) .
u~'-- 'i)(."'l
( y..'1._ 1 -xJ
- (~i--- -;;;
5
'
'I-.".. - ":);,(,_ --\ 5
)(1....,...., )(_ -7)(. --\
c)
(f. g)(x) .
d)
(f
e)
(go nc-3).
o
( )Y - ) ; ( '7-; y- 5 I
g)(x) .
C\ ~'2.- - IC:.)( - \ ':> -;.. --\ Z J
Gt 'f.--i. _ ,ur-' l '.)
C\( r;. r-5-:,
:ff( -~"- -l(l,.~ - 5
-q
c°' -c-w, -
-~( Oi.>r~ i-S
- "l (, l ';-s
- ,~ 5- 5
20. Find the inverse of each of the following fimctions:
a)
b)
f (x) = 3x 3
+5
~-=-- 3x7
S
Zx-1
g(x)=~