Beginning Algebra, 11th Edition

For the given information, (a)graph the inequality (here, and ,so graph only the

part of the inequality in quadrant I) and (b)give two ordered pairs that satisfy the inequality.

33.A company will ship xunits of merchandise to outlet I and yunits of merchandise to

outlet II. The company must ship a total of at least 500 units to these two outlets. The

preceding information can be expressed by writing

34.A toy manufacturer makes stuffed bears and geese. It takes 20 min to sew a bear and

30 min to sew a goose. There is a total of 480 min of sewing time available to make

xbears and ygeese. These restrictions lead to the inequality

20 x+ 30 y...480.

x+yÚ500.

xÚ 0 yÚ 0

SECTION 3.6 Introduction to Functions 229

Identifying Domains and Ranges of Relations

Identify the domain and range of each relation.

(a)

This relation has domain and

range The correspondence between

the elements of the domain and the elements of

the range is shown in FIGURE 41.

(b)

This relation has domain 536 and range { 5 , 6 , 7 , 8 }. NOW TRY

513 , 52 , 13 , 62 , 13 , 72 , 13 , 826

5 1, 2, 5, 8 6.

5 0, 2, 3, 4 6

51 0, 1 2 , 1 2, 5 2 , 1 3, 8 2 , 1 4, 2 26

EXAMPLE 1

NOW TRY ANSWER
1.domain: , 0, 2 ;
range: 3, 7, 8, 10 5 6

5 - 2 6

Find the value of for each given value of x. See Section 1.3.

35. 
    
    
    
    36. 
        
        
        
        37. 
            
        
        
        
        
    
    
    
    

38.- 39. 1 40.- 4

5

3

0 - 1 4

3 x^2 + 8 x+ 5

PREVIEW EXERCISES

OBJECTIVES

Introduction to Functions

3.6

1 Understand the

definition of a

relation.

2 Understand the

definition of a

function.

3 Decide whether an

equation defines a

function.

4 Find domains and

ranges.

5 Use function

notation.

6 Apply the function

concept in an

application.

If gasoline costs $3.00 per gal and we buy 1 gal, then we must pay

If we buy 2 gal, then the cost is If we buy 3 gal, then the cost is

and so on. Generalizing, if xrepresents the number of gallons,

then the cost is $3.00x. If we let yrepresent the cost, then the equation

relatesthe number of gallons, x, to the cost in dollars, y. The ordered pairs that

satisfy this equation form a relation.

OBJECTIVE 1 Understand the definition of a relation.In an ordered pair

xand yare called the componentsof the ordered pair. Any set of ordered pairs

is called a relation.The set of all first components of the ordered pairs of a relation

is the domainof the relation, and the set of all second components of the ordered

pairs is the rangeof the relation.

1 x, y 2 ,

1 x, y 2

y= 3.00x

$3.00 132 =$9.00,

$3.00 122 = $6.00.

$3.00 112 = $3.00.

NOW TRY
EXERCISE 1
Identify the domain and range
of the relation.

51 - 2, 3 2 , 1 0, 7 2 , 1 2, 8 2 , 1 2, 10 26

Domain Range

2

0

3

4

2

5

1

8

FIGURE 41