# MAT 115 Study Guide - Midterm Guide: Piecewise Linear Function, Function Composition, Asymptote

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8 Jun 2018
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Review for Exam #2
MAT115
Instructor: Steve Kish
1. For
2)( xxf
and
xxg 3)(
find a) (f+g)(x), b) (f-g)(x), c) (fg)(x), d) ,
 
x
g
f
,
e)
xgf
, f)
xfg
and the domain for each.
2. For the same f(x) and g(x) find a)
2 gf
, b)
3gf
, c)
2fg
,
d)
 
2
g
f
, e)
Sketch each graph
3.
xxf 3
1
)(
4.
32)( 2xxf
5.
21)( 2xxf
6.
 
11
2
12xxf
7. x = 2y2 + 1 8.
x
xf
3
1
)(
9.
x
xf 3)(
10.
1
2)(
x
xf
11.
13
2
1
)( xxf
12.
xxf 3
log)(
13.
xxf ln)(
14.
xxf 2
log3)(
15.
198)( 2 xxxf
16.
15)( 2 xxxf
17.
32
2
1
)( 2 xxxf
Solve each equation:
18.
xx 816
19.
121 8127 xx
20.
3log4x
21.
x3log
9
1
22.
16
4
1
x
23.
312 1000100 xx
24.
x
27
1
log3
25.
2
1
8
x
Expand the log as a sum or difference:
26.
3
2
4
log a
bx
27.
3
1
4
2
1
3
9
log
x
a
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