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Exercises
3
SEE EXAMPLE
p. 9
1
SEE EXAMPLE
p. 6
See
p. 8
Example
1-1
ä
x
KEYWORD: MB7 1-1
KEYWORD: MB7 Parent

1 (n - n) and n ∈ ); words
+_
8. x | x =1PRACTICE

GUIDED
2


9. Vocabulary Braces, { set-builder
notation
1.
}, are used in
? . (interval notation or roster notation)
−−−
È { Ó ä Ó { È
 the given numbers
 from least to greatest. Then classify each number by the
Order
10. 0,
5, 10, 15, 20,...; words
11. integers from -5 to 5; roster notation
 of1-1

subsets
the real numbers
to which it belongs.
Exercises
Sndependent
E E E X A M Practice
PLE 2
12–14
1
S E15–17
E E X A M P L2E
18–21
3
p. 9
x
Rewrite each set in the indicated notation.
For
Exercises
£x £ä
100 , -6.897, √#
3 , 4.−
1 , √#
2. 3 √#
2 , √#
7 , 5.125, 4_
6
3. -_
4, _
6
4
5
8
PRACTICE AND PROBLEM SOLVING
−
π , - √KEYWORD:
1
_
#
4. √#
5, _
3 , 1.3,MB7
-11-1
2
3
KEYWORD: MB7 Parent
Order
the given
numbers
from least
to greatest.
Then classify each number by the
Use
interval
notation
toGUIDED
represent
each
set of numbers.
PRACTICE
subsets
of
the
real
numbers
to
which
it
belongs.
the
set in{ the
indicated
notations.
cannot
be
5.Complete
-10 < x ≤
10table by1. writing
6.eachBraces,
7. notation
1 ≤Ifxa<set
or xnotation)
> 30
Vocabulary
}, are used
? . (interval
or20
roster
√#
−− 7
2ä in −−−
4 , -0.75 state
1 , -2,
_
_
£ä
x
x −−
in−
this
in
your
√5
#answer.
#, 2π, -1, 5.12, -_
#, -notation,
12.written
2.33, 5.
5,a2given
13. £x
-√
2
,_
, -1.
25 14. - √9
from least3to greatest. Then classify each number by the 2
S E E E X A M P L E 1 5 Order the given numbers
2
of thenotation.
real numbers to which it belongs.
p.in
6 the subsets
Rewrite each set
indicated
MB7 1-1
Words
Roster Notation
Interval Notation KEYWORD:
Set-Builder
Notation
−
−
100 , -6.897, √#
3 set
π , - √#
1 , √#
1
Useinterval notation to2.represent
each
3 √#
2 , √#
7 , 5.125,
4_
, 4.6 of numbers.
3. -_
4, _
6 4. √#
5, _
3 , 1.3, -1_

1 (n - n) and n ∈ ) ; words
4
5
8
2
3
_
x
|
x
=1
+
8.


?
{
-2,
-4,
-6,
-8,
...
}
?
?
26.
15. x ≠ 5
16. -15 < x < 0
17.
MB7 Parent
 to represent each set of numbers. ÈKEYWORD:
 S E E E X A M P2L E 2 Use interval notation
{ Ó ä Ó { È
9.27.
set-builder ?notation
?
[-4, 8)
?
p. 8
5. -10 < x ≤ 10
6.
7. 1 ≤ x < 20 or x > 30
GUIDED
PRACTICE
È {
Ó set
ä in
Ó the
{ indicated
È
Rewrite
each
notation.
£x £ä x
ä
x
Even numbers 
Vocabulary
? -5or
?
1.28.
Braces,
{
}
, are used? in ?11.
. (interval
notation
roster
notation)
10.
0,
5,
10,
15,
20,...
;
words
integers
from
to
5;
roster
notation


each set in the indicated
S Ebetween
E E3X] Aor
M P(L5,
E 11
3and
−−−19.notation.
27
39
18. (-∞,
]; Rewrite
words
positive multiples of 11; roster notation
Exercises
3
Extra Practice
Skills Practice p. S4
Application Practice p. S32

p. 9



1 (n - n) and n ∈ ) ; words
x | x =1
+_
8. from

Order
least
to?greatest. Then
classify
?
? each number{ xby| 0the
< x < 1}
20.29. the given numbers
2words


subsets
it belongs.
{ of
Îthe
Ó real
£ numbers
set-builder notation
ä £ 9. Ó Îto which
{
p. 6
PRACTICE
AND
È { Ó ä Ó { ÈSOLVING
−
 √#2 , √#7 , 5.125,
PROBLEM
100
3 , 4.
π , - √#
1 , √#
1
_
_
−
 , -6.897, √#
#
2.Express
3
4
6
3.
,_
4. √
5, _
, 1.3notation
, -1_
21.
-5,
-3,
-1
;
set-builder
notation
-9,

10.
0,
5,
10,
15,
20,...
;
words
11.6set-builder
integers
from
-5
to by
5; 3
roster
Order
the -7,
given
numbers
from
least
to
greatest.
Then4classify
each
number
the
ndependent Practice


each set of 5
numbers using interval
notation
and
notation.
4
8
2
3

 of the real numbers
  to which it belongs.
For
See
subsets
30.
31.
Exercises Example
√#
interval
set
of numbers.
Chemistry
Use
the4table
for
22–25.
−−Ó £ ä £ Ó Î { −− _
S E E E X A M P L E 2 Use
− notation
2 Elements
n È
{ Ó
1 , -2,
Î
äto
Órepresent
{ Exercises
È n each
_
PROBLEM
SOLVING
from
Periodic
Table
#
12. 2.33, 5.5, 2 √#
5 , -_
,PRACTICE
-0.75
13. AND
- √#
2 , _, {
-1.
25 14.
- √the
9 , 2π,
-1, 5.12
, -7
12–14
1
5
2
2
3
p. 8
Order
the
given
numbers
from
least
to
greatest.
Then
classify
each
number
by
the
Independent
Practice
5.
-10
<
x
≤
10
6.
7.
1
≤
x
<
20
or
x
>
22.
Order
the
given
elements
from
least
to
32. x ≤ 2 or 3 < x < 5
33. numbers between 1 and 10
15–17
2
30
For
See
Atomic
Mass MB7 1-1
Ionic
£x
£ä
x
subsets
of
the
real
numbers
to
which
it
belongs.
ä
x
KEYWORD:
greatest
atomic
Exercisesnotation
Example mass.
Use34.
interval
represent
18–21
3
√#
−−
−− 7
− each
2x ≤ 10
numbers
moreto
than
2 units
from
8 of numbers.
35.1 ,x-2,
≠ -5√and
4set
Element
Charge
#
12. 2.33, 5.5, 2 √#
5 , -_
, -0.75 13. _
2 , _, -1.25(amu)
14. - √#
9 , 2π, -1,
5.12, -_
12–14
1
5
2
3
Rewrite
each
set2 inofthe
S E E E X A M P L E 3 15.
23. xWhich
subset
theindicated
real numbers
best
≠ 515–17
16.notation.
-15
<x<0 2
17. KEYWORD: MB7 Parent
Extra Practice
Aluminum
26.982
+3
È { Ó ä Ó { È
these
Use masses
intervalisnotation
represent
each set
of numbers.
describes
18–21
31 atomic
the
of
p. 9
8.Tell
whether
each
statement
true
ortofalse.
If false,
give
a counterexample.
kills Practice p. S4
(n - n) and n ∈ ); words
x | x =1PRACTICE
+_
elements?
GUIDED
15.
x
≠
5
16.
-15
<
x
<
0
17.
Choose
from
/,
0,
1,
2,
and
).
Calcium
40.078
+2
eachPractice
set2in the
indicated
Rewrite
Extra
pplication Practice p. S32

36. Every
natural
number
is annotation.
integer.
37. Every real number
is irrational.
È { Ó ä Ó { È
Skills
Practice
p.
S4
9. Vocabulary Braces, { set-builder
notation
1.
, areset
used
in
? . (interval
notation or35.4527
roster
notation)
18.
in the
indicated
notation.
24.
subset
of
real}each
numbers
best
Chlorine
-1
Application
Practice
(Which
-∞,
or
(ä5,p. S32
11
;the
positive
11;irrational.
roster
notation
−−−19.39.
È
{3]Ó
38.
Every
integer
aRewrite
whole
number.
Everymultiples
integer is of
NOT
Ó ]is
{words
È
describes
the ionic18.
charges
of
these

(-∞, 3least
] or (5,to
11]greatest.
; words
19. positive
multiples ofby
11;the
roster notation
the
from
classify
each
S E E E X A M P L E 1 Order
Lithium
+1
10. 0,
5, given
10, 15,numbers
20,...; words
11.Then
integers
from
-5 number
to6.941
5; roster notation
20.
words
elements?
Choose
from
/,
0,
1,
2,
and
).
20.
words
Îthe
Ó
£
{ of
ätable
£ Ó
Îto which
{ ball
Sports
Usereal
thenumbers
of soccer
subsets
it belongs.
p. 6
{ Î Ó £ ä £ Ó Î {
Sizes
Sulfur Soccer Ball
32.066
Explain
 notation
for Exercises
40–42.
−
− -2 1-1
25.sizes
why interval
cannot
100 ,-6.897, √#
3 , 4.
π , - √KEYWORD:
1 , √#
1
_
_
_
_
√
√
√
#
#
#
#
2. 3
2
,
7
,
5.125,
4
6
3.
4
,
6
4.
5
,
3 , 1.3,MB7
-15_
21.
-9,
-7,
-5,
-3,
-1
;
set-builder
notation


21.
-9, -7, -5, -3, -1 ; Size
set-builder notation

3
4
4
5
8
2
3
be
used
to
represent
the
set
of
atomic

 SOLVING
 Identify theAND
40.
size of PROBLEM
each
ball:
PRACTICE
KEYWORD: MB714–16
Parent
Weight
(oz)22–25.
11–12
12–13
masses
given.
Chemistry
Use the
for Exercises
Order
the
given
from
least
totable
greatest.
Then
classify
each
number
byPeriodic
the Table
Elements
from the
Chemistry
Use
the
table
forradius
Exercises
22–25.
interval
notation
toGUIDED
represent
each
set
of numbers.
Sndependent
E E E X A M Practice
P L E 2 Use
soccer
ballnumbers
A: 4.36
in.
Elements
from
the
Periodic
Table
PRACTICE
22. Order
given it
elements
from least to
For
See
Circumference
subsets
of the
real
numbers
to the
which
belongs.
Atomic
Mass
Ionic
the
by1. in.
writing
each
set
indicated
notations.
set
cannot
be
23–24
25–26
27–28
p. 8
22.
Order
given
from
least
toin{ the
Exercises Example
5.Complete
-10
<the
x≤
10table
6.
7. notation
1 ≤Ifxa<
or
xnotation)
> 30
greatest
atomic
mass.
soccer
ball
B:elements
7.54
diameter
Vocabulary
Braces,
}, are used
in ? . (interval
or20
roster
(in.)
√#
Element
(amu)
Charge
−−−
−−
−−
− a given
2
Atomic Mass
Ionic
7
4
1
_
_
_
£x
£ä
x
ä
x
written
in
notation,
state
this
in
your
answer.
√#
mass.
12. greatest
2.33,
5.5atomic
, ball
2 √#
5, ,23.
-0.75
13. of,the
-2,
-numbers
2,
, -1.25 14. - √#
9 , 2π, -1, 5.12, -_
3 subset
0 12–14
Chapter11 Foundations
for
Functions
Which
real
best
inthe
volume
given numbers
from
least
greatest.Under
Then
classify
each
numberCharge
by Over
the +32
Ssoccer
EE EXAM
P L E C:1 276.2
(amu)
5 Order
2
3toElement
Aluminum
26.982
Age
of
Player
8
8–12
12
describes
the
masses
of these
subsets
of thenotation.
realatomic
numbers
to which
it belongs.
p.in
6 ofthe
23.41.
Which
subset
the
real
numbers
best
each
set
indicated
S E15–17
E E X A M P L2E 3 Rewrite
Words
Roster
Notation
Interval
Notation
Set-Builder
Notation
elements?
Choose
from
/,
0,
1,
2,
and
).
Calcium
40.078
Use set-builder
notation
to each_3set− of numbers.
Aluminum
+3− +2 1
100 , -6.897, √#
π , - √#
1 ,26.982
Usedescribes
interval
notation
to
18–21
3
√#
2.represent
3 √#
2 , √#
7 ,of
5.125,
4 , 4.6
3. -_
4, _
6 4. √#
5, _
3 , 1.3, -1_
the
atomic
masses
these
p. 9
1
4
5
8
2
_
represent
the
weight
range
for
each
soccer
ball
size.
24.
Which
subset
of
the
real
numbers
best
Chlorine
35.4527
(?n - n) and n{-2,
| x5=1 +Choose
∈16.
)
words
8.26.
;2,
elements?
-4,
-6,
...0
} Calcium ? 17. 40.078
?+2 -1 3
15.
xx ≠
-15
<-8,
x).<
from
/, 0,
1,
and
2
describes
the
ionic
charges
of these
Extra Practice


notation tothe
represent
each setfor
of numbers.
LithiumÈ { Ó
6.941ä Ó { +1
E E Einterval
X A M P L E notation
2 Use interval
È
42. SUse
to represent
age
each
elements?
Choose
from /,
0, range
1, 2, and
).[9.27.
set-builder
?
?notation
4, 8)soccer ball size. ?
Skills
Practice p. S4 10
1_0006_0013.indd
p. 8 of the5.
24.
Which subset
real
35.4527
-1
-10numbers
< x ≤ 10 best
6. Chlorine
7. 132.066
≤ x < 20 or
x >-2
30 9/8/05 3:26:22 PM
Sulfur
È {
Ó set
ä in
Ó the
{ indicated
È Explain why
Rewrite
each
notation.
Application Practice p. S32
interval
cannot
£x £ä number
x
ä
x
43.
Theof
product
ofnotation
an irrational
and
a rational number describes
theThinking
ionic25.
charges
these
Even numbers
 Critical
be used to represent
the set of atomic
?
? -5 to
?+1
28.
Lithium
6.941
10.
0,
5,
10,
15,
20,...
;
words
11.
integers
from
5;
roster
notation


is
an
irrational
number.
Explain
why
this
means
that
no
matter
how
precisely
you
Rewrite
set
theand
indicated
S Ebetween
E E3X] Aor
MChoose
P(L5,
E 11
3and
27
39masses
/,each
0,given.
1, in
2,
).19.notation.
18. elements?
(-∞,
]; from
words
positive multiples of 11;
roster
notation
 measurep.the



9 diameter
of
a
soccer
ball,
your
calculation
for
its
circumference
will
1
32.066
words
8. x | x =1 + _(n -? n) and n ∈ ); Sulfur
?
?
{ x | 0 < -2
x < 1}
25.
Explain
why
notation
cannot
20.29.
2words

 number.
NEVER
beinterval
a rational
{
Î
Ó
£
9.
set-builder
notation
10
Chapter
1
Foundations
for
Functions
ä
£
Ó
Î
{
be used to represent
set of atomic PRACTICE
AND the
PROBLEM
È { Ó ä Ó { ÈSOLVING



masses
given.
21.Express
-5,
-3,
;0,set-builder
notation
-9,
10.from
5, 10,
15, 20,...
11. set-builder
integers
from -5
to by
5; roster
Order
the -7,
given
numbers
least
tointerval
greatest.
Then classify
each number
the notation
ndependent Practice
; words notation
each
set
of -1
numbers
using
and
notation.




For
See
subsets
of
the
real
numbers
to
which
it
belongs.
44. This problem will prepare you for the Multi-Step
Test Prep on page 42.
30.
31.
Exercises Example
√#
a207se_c01l01_0006_0013.indd
9/8/05 3:26:22 PM
Chemistry
the_
table
for
Exercises
22–25.
−−Ó £ ä £ Ó Î { −− _
− Use
2
n
È
{10Ó
4
1
{
Î
ä
Ó
{
È
n
_
_
PRACTICE
AND
PROBLEM
SOLVING
0 12–14
Chapter11 Foundations
for
Functions
√
Elements
from
Periodic
Table
#
12. 2.33,
5.5, 2 √#
5in
,, -0.75
13.measured
, -2, -in #
2,
, -1.
25 14.
- √the
9 , 2π,
-1, 5.12
, -7
Distances
space
are often
5
2
2
3
Average
Distances
frombyEarth
the from
given numbers
greatest.
Then
classify
each
number
Independent
22.32.Order
given
least tofrom least
x ≤ 2the
orPractice
3 < x elements
< Order
5
33. tonumbers
between
1 and
10
15–17
2
the
astronomical
units
(AU).
AUnumbers
is defined
as it belongs.
For
See
Atomic Mass
Ionic
subsets
of One
the real
to which
greatest
atomic
mass.
Exercisesnotation
Example
DistanceCharge
(AU)−− 7
Use34.
interval
to
represent
of the
numbers.
18–21
3
√Body
#
−−
− each
2x ≤ 10
the
average
distance
between
Earth
Sun.
numbers
more
than
2 units
from
8 and
35.
≠ -5√and
4set
1 ,x-2,
Element
#
12. 2.33, 5.5, 2 √#
5 , -_
, -0.75 13. _
2 , _, -1.25(amu)
14. - √#
9 , 2π, -1, 5.12, -_
12–14
1
5
2
2
3
23. xWhich
the realofnumbers
best
15.
≠a.515–17
16. real
-15
< x < 0 do
17.
97
2 ofsubsets
_
Tosubset
which
the
numbers
Mars
Extra Practice
Aluminum
26.982
+3
È
{
Ó
Ó { È
Use
interval
represent
each set
of numbers.
18–21
3 atomic
describes
the
of
these
Tell
whether
each
statement
isnotation
true
ortofalse.
If false,
give
a counterexample.ä 186
the numbers
inmasses
the table
belong?
kills Practice p. S4 10
1_0006_0013.indd
9/8/05 3:26:22 PM
15.
x
≠
5
16.
-15
<
x
<
0
17.
elements?
Choose
from
/,
0,
1,
2,
and
).
Calcium
40.078
+2
117
Rewrite
each
set
in
the
indicated
notation.
_
Extra
Practice
pplication Practice p. S32
36. Every
natural
number
is
an
integer.
37.
Every
real
number
is
irrational.
b. Order the bodies from least to greatest
Mercury
È { Ó ä Ó { È
Skills Practice p. S4
310
average
distance
from
Earth.
Rewrite
each
set
in the
indicated
notation.
24.38.
subset
of
the
real
numbers
best
Chlorine
35.4527
-1
Application
Practice
p. S32
18.
(Which
-∞,
3
]
or
(
5,
11
]
;
words
19.
positive
multiples
of
11;
roster
notation
Every integer is a whole number.
39. Every integer is NOT irrational.
SEE EXAMPLE
1-1
1
Exercises
1-1
Exercises
Moon
0.0026