Micitcriii 1 Review
Answer each of the following:
1. Is {3,
,
/}
—271,
/%/\
Q? Why or why not?
C
(-7 / 9
2. What is {1,7,S} —{1,8,9}?
.-..
.
A
3. Is [0, no)
C
JR
—
{ir} a true statement? Why or why not?
ir to a:)
se
4. Is [—17, no)
C (—li
‘ti3-
‘ou1-
,
no) a true statement.? W by or why not.
5. Find 3 things that are
[2, —1] E [—no, no)
wrong
Lz-] sL&\d
T-e s-o
c ‘—4
-\]
— -l1
c—i—
with the following statement:
oe
c4-e ci!
i
‘
be
[2]
“
S’i(Q
-r’-e
—\-Z.
rS-j-
ijf
‘a
C&
e
eed
6. Suppose
f:N
JR is defined by f(n)
—
(a) n is an object of which set? (Rational numbers, Integers. Real numbers. or Natural numbers?)
r\
6 fj
S’
(b) What is f(2
#
L
‘
7
(c) What is f(—3)?
-& &
i’-ed s’c2
—3
For #7-10, state if the sequence is arithmetic, geometric, or neither.
7. 3,30, 300,3000,
eorrcii S’mce.
\DO...-
8. ,4,9,16,...
9. 27.21,15.9,...
s\ce
10. 40,10,
.
For #11—14, find the indicated term:
11. If a.
12. If a
—
—
ck
3,12
3
—
—
2, find
08
10
, find a
2
n
2.
1
13. What is the
th
27
term in the sequence —10, —7, —4,—i,...?
rd
23
term in the se uen
co
i4. \Vhat is the
Z7
Foi #15 23, find the indicated
(-
tr
-1+(2(3
48 24 12 6,...?
ArQh c_
3
M
&eet
ç
—
L%)
sum.
i5.Z4
N
16. Z(-2i+1)
,,,
+
s”
1..
SAv—- Df
(_
4(-+(-zi
17.
4
S.z
_-3
d:-2.
-(c
=
of
‘
r
9
=
-
I
0
18.
i=1
of
SUrv
QM2
9
00
z
4-”
i=1
=
S=
What
S\Arv\
is the sum of the first 83 terms for 91 + 86 + 81 + 76 + ...?
D
s=
\Ailtv-
e-e-t-r’iC
a
+
21. Find the sum of the following infinite series: 81 + 27 + 9 + 3 + ...?
S\-r\
cA
---
Lz)z
3
20.
I-\y-_h C
r4
UJ*
()c
YL
C
91—’)
(-z2’)
UL
V
3
2..
=
((-sN
Ztz
“
22. Find the
sum
o-
of the following infinite series: 25 + 15 + 9 +
2-55
+
w
ec
\5
-
s
23. Find the sum of the following infinite
r’
c$
series:
± 1 + 2 + 1 +
’hf
1
\
-
(2.,
--
Answer each of the following:
24. You’re on vacation and have brought with you 3 pairs of shorts, 4 shirts, and 2 pairs of shoes. How
many different outfits can you make?
Di
ce
SNO
H-
=3
25. There are 18 jelly-bellies in a jar, each are different flavors. How many different ways can you select 4
jelly-bellies?
Oir
a.oer.’-1- --4-€(
L\
-
(rL\
‘!‘1’1o” ‘
C
26. There are 100 sales people at a large corporation. The president of the corporation has decided she
will select a head of sales, assistant to the head of sales, and secretary from the pool of 100. How many
different options does the president have?
AD5+
ç:
I
cfS a
I
W
Z’,
27. If you have 4 different gifts and you want to give each one of your 4 best friends one of them, how many
different ways can you give your lfts?
‘\Fie
r’r\c&1eSJ
“ jCCf
OOAS
2
ç’i
28. You work for a large corporation that likes to give gifts to politicians. rfhere is a pooi of 12 different
gifts that you can give and you have to select a specific gift for three different people. How many ways
could you give the gifts?
a
7’r eCtS
0
L’Li dceie-)
Jc 2-
3
(-€r\
29. You just got your first credit card and need to choose a four-digit pin number.
(a) Assuming you must use 0
pin numbers are there?
—
9 for each digit but there are no other restrictions, how many possible
1
(b) You’ve decided that you want a pin number where the four digits are unique (no repeated digits).
How many possible pin numbers, are there if you make this restriction?
30. There are 10 people interested in learning how to use a new interactive technology, but the instructor
can only train 3 people. I-Tow many ways might she choose the three people?
/V
aces\ ‘+
-
(3
-
‘
7/’
-
31. You’re at the gym and need to work out your arms, abs, and legs. There are 3 machines for arms, 2 for
abs, and 6 for legs. You only have time to use one machine for each area (arms, abs, and legs). how
many different ways could you select the machines you will use?
32. What is
I
(12)7
—_
-
Sy33. Write (x
‘
—
.cç
/Y-\
/\
J
—.
r’-
Lj-
/ \
(-3)
(\
2xT
Jx—,
UI
bc)
+-
(a)
-
3)4 in expanded notation using the binomial theorem.
‘
34. If f(x)
I
—
(-k
(j
vat is:
oy()
(b) gof(x)
4
(-N
II
cC
-
ii
—}4.
I
‘I
c-.
C’-.
oI3
cc
-
cC
WI
0
:1*zI I
(
-1
V
0
-d
C
5
v-c
C
LCD
For #39-45 graph and state the domain and range of each.
39.f(x)=x
R=
‘1’
40. 1(x)
=
-
2
_; -•‘1
R=
-L
-2
-4
‘0
41. f(x)
=
R= Lo, a
6
iJ’j
L
0
c’
(O
cç
\-‘?
cQQ2=H
-z
T
-=cI
t’
•J7J7
7
t
a
‘1\iJO
1j
‘1)
‘V
0—H
I)
Q-=G
—
jO—
(x)f
1
\
a
0
=
(x)[
J7
4.5.
g: Hi, 2)
—
R where g(.x)
D=
=
—.\
-1
=
[oi)
0
C)
7
H
2’j
-1
Use graph transformations to graph #46-47 and state the domain and range of each. Make sure to explain
the transformation in words as well.
c-M--CtsLV
46. Ii(x)
=
—2
3
©j&CcQ -\-: ±11
O’J(
Th
-/7
-
z:
—
z
‘“
D
—2.
0
—
47.
f(x) (x
=
—
2)2 + 3
iQ
D=
2
:
I’f\
oir*’
—
9
1
8
+