can someone help me tonight?
rollinbrittany
ws_3_-_review_for_final_exam.docPRECALCULUS
MTH 112 –WORKSHEET # 3 – REVIEW FOR FINAL EXAM
NAME:__________________________DATE:__________CLASS TIME:__________
Answer each of the following problems on a SCANTRON answer sheet. This assignment will be graded. Work all problems on your own paper, neatly and in order. Turn in work paper stapled. Also turn in Scantron answer sheet sheet separately. Do not staple Scantron to work paper! Work paper may also be graded. This worksheet is worth 40 points.
(
)
(
)
2
1) For 834, find 1.
gtttg
=+--
a) 11
-
b) 1
-
c) 1
d) 9
(
)
(
)
2
2) For 834, find .
gtttgs
=+-
a) 8
s
+
2
b) 438
ss
-++
c) 7
d) 0
(
)
(
)
3
3) For ()1 and ()3, find 1.
fxxgxxfg
=+=++
a) 5
b) 6
c) 7
d) 8
(
)
(
)
3
4) For ()1 and ()3, find 2.
fxxgxxfg
=+=+
o
a) 26
b) 45
c) 126
d) 216
2
()()
5) For ()2, find .
fxhfx
fxx
h
+-
=-
a) 1
b) 2
xh
+
2
24
c)
xhh
h
+-
d) 21
xh
-
6) For ()21, evaluate at 2.
x
fxxx
=++=
a) 6
b) 7
c) 8
d) 9
3
7) For ()log, evaluate at 27. (This
can be done without a calculator.)
fxxx
==
.
a) 3
b) 6
c) 9
d) 24
8) Rewrite log in exponential form.
S
TR
=
a)
R
TS
=
b)
S
TR
=
c)
S
RT
=
d)
R
ST
=
32
2
3
9) Use the properties of logarithms to
expand the following expression as a sum
,
difference, and/or constant multipl
e of logarithms: log.
xy
z
222
111
a) logloglog
323
xyz
-+
222
111
b) logloglog
323
xyz
+-
222
c) 3log2log3log
xyz
+-
222
d) 3log2log3log
xyz
-+
4
10) Evaluate the following using the ch
ange-of-base formula and a calculator:
log18.
Round to the nearest hundredth.
a) 0.48
b) 0.65
c) 2.08
d) 4.50
232
11) Solve the following system of linea
r equations: .
431
xy
xy
+=-
ì
í
+=-
î
1
a) ,1
2
æö
-
ç÷
èø
35
b) ,
23
æö
-
ç÷
èø
15
c) ,
69
æö
--
ç÷
èø
(
)
d) 1,0
-
2
12) Solve the following quadratic inequ
ality: 45.
xx
+<
(
)
a) ,
-¥¥
(
)
(
)
b) ,51,
-¥-¥
U
c) No Solution
(
)
d) 5,1
-
2
13) Solve for : 32.
xxxx
+=--
a) 22
-±
b) 13
-±
c) 2
-
(
)
d) 2,2
-
2
14) Solve for : 613.
xxx
=--
613
a)
4
i
-±
b) 32
i
-±
c) 322
±
62
d)
2
±
15) Solve for : 81423.
xxx
+³--
11
a) ,
2
æù
-¥-
ç
ú
èû
11
b) ,
2
éö
-¥
÷
ê
ëø
(
]
c) ,2
-¥-
[
)
d) 2,
-¥
16) Find the slope of the line: 382.
xy
-=
1
a)
4
b) 4
-
3
c)
8
8
d)
3
-
(
)
(
)
(
)
(
)
17) Determine if the lines through the
following points are parallel, perpendic
ular,
or neither. Line A: 4,5 and 8
,8; Line B: 6,2 and 3,2
-
a) parallel
b) perpendicular
c) neither
(
)
1
18) Find an equation in Standard Form f
or the line with and passing
3
through the point 1,6.
m
=-
-
a) 317
xy
+=
b) 317
xy
+=-
c) 33
xy
+=
d) 33
xy
+=-
19) Does the graph shown depict as a f
unction of ?
yx
a) yes
b) no
(
)
(
)
2
36, 3
20) Given , find 3.
1, 3
xx
fxf
xx
-£-
ì
=-
í
+>-
î
a) 8
b) 10
c) 15
-
d) 3
-
(
)
(
)
(
)
(
)
3
21) Given 2+2 and 1, find 1.
fxxgxxgf
==+-
o
a) 0
b) 1
c) 2
d) 3
(
)
(
)
22
22) Find the center and radius for the
following circle: 1625.
xy
-++=
(
)
a) 1,6, 5
Cr
=-=
(
)
b) 1,6, 25
Cr
=-=
(
)
c) 1,6, 5
Cr
=-=
(
)
d) 1,6, 25
Cr
=-=
2
23) Find the vertex of the following pa
rabola: 225.
yxx
=-+
19
a) ,
22
æö
ç÷
èø
111
b) ,
22
æö
-
ç÷
èø
113
c) ,
22
æö
-
ç÷
èø
17
d) ,
22
æö
--
ç÷
èø
(
)
(
)
32
24) Divide using synthetic division:
2722.
xxxx
+--¸-
2
12
a) 7
2
x
x
-+
-
2
b) 41
xx
++
2
c) 7
x
-
2
4
d) 41
2
xx
x
++-
-
32
25) Find all rational roots of the equa
tion: 21310.
xxx
+-+
(
)
a) 10,5,1,2
--
(
)
b) 5,1,2
-
11
c) 2,,,1
510
æö
--
ç÷
èø
1
d) 2,,1
10
æö
-
ç÷
èø
(
)
3
16
26) Find any vertical asymptotes: .
8
x
fx
x
-
=
-
a) 0
x
=
b) 2
x
=
c) 16
x
=
d) none
(
)
3
16
27) Find any horizontal asymptotes: .
8
x
fx
x
-
=
-
a) 0
y
=
b) 2
y
=
c) 16
y
=
d) none
(
)
2
6
28) Find any slant asymptotes: .
4
x
fx
x
-
=
+
a) 4
yx
=-
b) 6
yx
=-
c) 10
yx
=-
d) 22
yx
=-
3
29) Evaluate log3.
a) 3
-
b) 0
c) 1
d) 9
6
30) Evaluate log1.
a) 0
b) 1
c) 6
d) 36
4
31) Evaluate log16.
a) 2
b) 4
c) 16
d) 64
32) Evaluate log15. (Round to the near
est hundredth when necessary.)
a) 0.43
b) 1.18
c) 1.53
d) 2.71
33) Evaluate ln65.35. (Round to the ne
arest hundredth when necessary.)
a) 0.60
b) 1.82
c) 3.93
d) 4.18
2
34) Evaluate 5. (Round to the nearest
hundredth when necessary.)
e
a) 25.00
b) 36.95
c) 67.96
d) 296.83
35) Evaluate . (Round to the nearest h
undredth when necessary.)
e
a) No Solution
b) 0.72
c) 1.36
d) 1.65
2
36) Write the following in logarithmic
form: 3=9.
3
a) log29
=
3
b) log92
=
2
c) log93
=
9
d) log23
=
4
8
37) Expand the following using logarith
mic properties: log.
W
xy
z
1
a) 4loglog8log
2
WWW
xyz
+-
11
b) log2loglog
48
WWW
xyz
+-
1
c) 4loglog8log
2
WWW
xyz
--+
11
d) log2loglog
48
WWW
xyz
--+
1
38) Condense the following using logari
thmic properties: loglog6log.
5
AAA
bcd
+-
6
5
a) log
A
bd
c
6
5
b) log
A
bd
c
5
6
c) log
A
bc
d
5
6
d) log
A
bc
d
248
39) Solve the system of linear equation
s: .
346
xy
xy
+=
ì
í
+=
î
3
a) 1,
2
æö
ç÷
èø
(
)
b) 2,3
-
(
)
c) ,
-¥¥
d) No Solution
1
3
40) Solve the system of linear equation
s: .
2
218
xy
xy
ì
+=
ï
í
ï
+=
î
(
)
a) 3,0
(
)
b) 1,15
(
)
c) ,
-¥¥
d) No Solution
