Intermediate Algebra (11th edition)

OBJECTIVE 3 Find the domain and range.For every relation, there are two

important sets of elements called the domainand range.

184 CHAPTER 3 Graphs, Linear Equations, and Functions

Finding Domains and Ranges of Relations

Give the domain and range of each relation. Tell whether the relation defines a

function.

(a)

The domain, the set of x-values, is The range, the set of y-values, is

This relation is not a function because the same x-value 4 is paired

with two different y-values, 2 and 5.

5 - 1 , 2 , 5 , 86.

53 , 4 , 66.

513 , - 12 , 14 , 22 , 14 , 52 , 16 , 826

EXAMPLE 2

(b)

The domain of the relation represented

by this mapping is , and

the range is The mapping

defines a function — each domain value

corresponds to exactly one range value.

(c)

In this table, the domain is the set of

x-values and the range is the

set of y-values. The table defines a

function — each x-value corresponds to

exactly one y-value (even though it is the

same y-value).

526

5 - 5, 0, 5 6

5 A, B, C 6.

5 95, 89, 88, 78 6

Domain and Range

In a relation, the set of all values of the independent variable is the domain.

The set of all values of the dependent variable 1 y 2 is the range.

1 x 2

(^95) A
89
88 B
(^78) C
xy
52
02
52

• 
  

NOW TRY

A graph gives a “picture” of a relation and can be used to determine its domain

and range.

(a)

This relation includes the four

ordered pairs that are graphed. The

domain is the set of x-values,

The range is the set of y-values,

(b)

The x-values of the points on the

graph include all numbers between

and 4, inclusive. The y-values include all

numbers between and 6, inclusive.

The domain is.

The range is 3 - 6 , 64.

3 - 4 , 44

- 6

- 4

5 - 3 , - 1 , 1 , 26.

5 - 1 , 0 , 1 , 46.

x

y

0

( 0 , –1)

( 4 , –3)

(–1, 1 )

( 1 , 2 )

Use interval

notation.

x

y

–4^0

–6

6

4

Range

Domain

Finding Domains and Ranges from Graphs

Give the domain and range of each relation.

EXAMPLE 3

NOW TRY
EXERCISE 2
Give the domain and range of
each relation. Tell whether the
relation defines a function.

(a)

(b)

1 6, 5 26

51 2, 2 2 , 1 2, 5 2 , 1 4, 8 2 ,

xy

1 $ 1.39

10 $10.39

15 $20.85

NOW TRY ANSWERS

2. (a)domain: ;
   range: ;
   not a function
   (b)domain: ;
   range: ;
   function

5 $1.39, $10.39, $20.85 6

5 1, 10, 15 6

5 2, 5, 8 6

5 2, 4, 6 6