Final Review
Discrete Math
For #1-5 find the specific term:
1) Find the
th
18
term for: 67, 61, 55,
(—a
’’s
0
4
2) Find the
st
21
(ii(-
term for: —14, —10, —6,
O.
1
CA
-
-I
-l
3) Find the
rd
83
term for: 16, 8,4,
C
Q
.
1
(c
o&3
I.
O- t(,
term for: —3,6, —12, 24,
4) Find the
C-.
3
5) Find the
nd
32
term for:
, , ,
\(
a•r
(3
For #6-12 find the given sum:
4
—‘
3
a
P5
1
4
LI_I
/
‘
9-’\-
II
I°
TICO
Hc)
•1
3
c
OD
1’
H
‘I
OJ
I’
cy3
p
C,
Lj’
£
+
+
+
C
CD
CD
‘I
-ii
03
9J
3
-
-s
3’
+
CD
C)
+
+
C
SCi:,
CD
CD
CI)
CD
C
3
—
“
-‘
—
-r
-
Q)
(J-
-::
4.
-,
cp
+
+
I
+
C
ci:,
CD
Cl)
-I
-
CD
CD
-
H
H
“
D)
-
(r
C,
-:r
t’,DICi)
f: -
I
—
Cl’
•
(JI
Co
,—‘
-41
i—’
-
‘I
Cl
2
For #13-21 find the following:
13) You’re at Café Rio and want to order a burrito. There are three kinds of beans, two types of rice, and
four kinds of meat fillings for the burrito. How many different kinds of burritos can you make if you select
one of each? (You don’t need to simplify)
3
14) Write
()
as an integer.
q
9
:
_L\.
-
15) Suppose a set A contains 243 objects. How many 92 object subsets of A are there? (You don’t need to
simplify)
43
a
4’
Jo4
chc,ocz-
i
v’o
c,(&_1
Oje
(p3)
-4c
16) How many ways are there to choose and order 49 objects from a collection of 304 objects? (You don’t
need to simplify)
119
O’..-r
-
(r’- \‘-“
17) How many different 4 letter words can you make with the letters MATH i
don’t need to simplify)
3
or a
ouuse each letter once? (You
i
18) How many different ways can you order 21 different objects? (You don’t need to simplify)
4Eii1
19) There are 20 people competing for 3 scholarships each worth $5000 per year. How many different ways
can you select three different people? (You don’t need to simplify)
(D\\
(o—3). 3’.
20) There are 20 people competing for a $1000, $3000, and $5000 scholarship. How many different ways can
you select the three different people? (You don’t need to simplify)
Dra
r1_’k(
3
21) How many 3 people committees can you make from 12 people? (You don’t need to simplify)
(ve,kkR(
2±
/ Q\
3
)
—
I
3
-
Graphing
Graph and state the x-intercept(s), y-intercept, domain (D), range (B), leading term (LT), end behavior
(EB), or vertical asymptote (VA) when specified:
22) Graph
f(x)
23) Graph
2
f(x)
=
z
I
1.—.
...
-
LI
.
.
F
P!
!!
-r
TI
x-int(s)= YorQ.
y-int=
D=_______ R=_______
24) Graph
f(x)
25) Graph
=
1
.
x-int(s)=_
y-int=
D=________ R=________
————r
f(x)
=
1
I
I.
x-int(s))’
0
D=
R=
.
x-int(s)=
y-int= ‘/
bcø
LI
4
y-int=
R=________
-
-
L
C
C.)
C
C
C
C
C
C
C
C
C
0
CD
C’]
-
;j
—
.--
-——
-—
.-.--.-.-—--—-—..—-
+
I
-44
4
E
-‘-
0
0
Co
C’]
liii
: :1: : : :
Ti
I
-
-
:jzzJ,
-I
ilIf
11111
.4.. 1
C
C
CjA
9
II
A
II
C
II
C)
C)
0
0
C
II
uD
(‘a’
t.
0
r
c,
—
0
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r
III
C,,
Jn 111
•h
Li
-r
d
I
÷—,
4-
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Ei
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C)
4.
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II
IQ
C)
cz
>J
‘I
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p
,J
I’
Q
-U
:
:z
1
-4-- -
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E
II
Ct,
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-
CD
CD
-I
‘—
II
2C)
‘‘
:3
.
1
P
0
fLJ’
0
f”?
36) Graph n(x)
i1-’r
‘1
D’I-(
37) Graph
=
h(x)
=
—\/Ti + 2
r
y-int=
x-int(s)=
1&
D=
(j’;
‘1
x-int(s =
D=_______ 11=
y-int=
T;-c3
—
L4
)C:
3
39) Graph p(x)
=
iL
38) Graph m(x)
=
4(x + 2)2 + 1
x-int(s)= v1’L—
v-int=
D=____ R=
vertex= (E ‘?
/;
1)
—2(x+1)(x+1)(x—2)(x
+
2
x-int(s)=
\/ H
LT=_______
y-irit=
1}
-
7
((-) (i 9
-
H
ci
1+
H
H
8
U)
H
II
H
w
—
H
—
H
: :: :: :: ::
,1IUJ
.
I4W
i ii
E
II
-d
cJD
c’1
H
4_
H
VI A
H
-
H
0
(
•
LJr.
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C
4J
0
cy)
d
S
C
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co
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cD
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1)
-
co
z
0
&
(3
..1
9J
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k
((V
3
9J
—4(
II
C)1
+
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—
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3-)
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Co
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H
>c
J
I
Co
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II
+
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CD
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CD
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cT
ci
w
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0
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0
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cjq
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CD
I
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2
50) Find z where (23’5) (3)
O3
2
=
c)
-
I-”
-
Ys
‘2
4-
oa()
3
,c
-.-
3
51) Find
i
x)
log
(
where 9
1
log
(
9
—
—
x)
=
3
,
Eli
‘(5
B
) +8
3
52) Find x 41og( + 1og(x
11
=
)
3
e°(
3
(5)
(.):
e
1
i
53) Find x where 2
=
£
e
e
x
31og
(
8
—
)<-J
,.
1)
—
8
(-i
)
8
x-
54) Find g o
f(x)
if
f(x)
=
.L{
x + 3 and g(i)
3
Ei
=
Ei:iii1
55) Find the inverse of g(x)
=
2/Tx
)(
-
10
3
56) Find the inverse of rn(z)
31og(5
=
(c-’)
2x)
—
.,
1
3o32
Svtc
—
3
57) Find the implied domain for p(x)
rio
i c-,,
Ioo 4
=
o.ç
v.J€
c’j4 ‘
58) Find the implied domain for a(x)
\-()
59) Find the implied domain of
flo
= 2_4
0
iL
ç_
iEEiEZ5
flQQ
0’
f(x)
= 12
—
31
+ log(4
—
5x)
0
EEZIEE1
4/5
5c4
60) Find the implied domain of g(x)
H
=
ç
—
No
61) Complete the square: write 212
—
4x
—
3 in the form of a(x +
/3)2
+ 7 where c, /3,-y E R.
2
CC3
-
11
-
V
—
>
Uj
—
>c
1
I.’
)
x
Co
9__)
+
L
,
—
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U)
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5
lb
5
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p
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IJ
l.=.
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c
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i9-)
bs
p
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;c
1
C
4
+
+
p
-
-
0
0
c,.
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f—
0
II
CD
CD
0
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cc
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ry
I’
c”)
—
1’
r_
c(7
—\
II
72) Find
—1
(_3
1
2”
4)
al
‘--i
3
dL
I
A -‘
/1
73) Find det 0
(
—2
1
0
-
2 -3
çL..1
-
_1L1
[3
_Lt_
(-(i;)
_H
i
-‘
_3\
—1
2)
1
i[’
(1
L
a
(-i
—
-
74) Write the following system of three linear equations in three variables as a matrix equatioiT
y+z = 2
y + 2z = 1
—x+y—z=O
2x
—
-
-
I
Li
LH
75) Solve for x,y,z if:
2
(—1
(—2
2
\3-1
f
—f\
/—2’\
(—1
—1)(y)=( 2 )andf_2
1JzJ
\3
\iJ
2
—1’\
2
_i)
-11)
1
/1
=(_i
\-4
—1 0
2
1
52
--
z)
[x 1
I
I
I
ll_V
hi
Lzi L9
-2
Li
+
-i
2
5
•‘
1.1
(
aoy