Intermediate Algebra (11th edition)

Relations and functions can be defined in several different ways.

• As a set of ordered pairs (See Example 1.)


• As a correspondence ormapping

SECTION 3.5 Introduction to Relations and Functions 183

1

3

2

4

Relation F

F is a function.

–2

–1

24

22

1

0

Relation H

H is not a function.

FIGURE 43

See FIGURE 43. In the mapping for relation FfromExample 1(a),1 is mapped to 2,

is mapped to 4, and 3 is mapped to Thus, Fis a function, since each first

component is paired with exactly one second component. In the mapping for rela-

tion Hfrom Example 1(c),which is not a function, the first component is

paired with two different second components.

- 2

- 2 - 1.

x

y

(^0) (3, 2 1)
( 2 2, 4)
(1, 2)
Graph of relation F
FIGURE 44
xy
12
24
31 -

• 
  

Table for

relation F

• As an equation (or rule)

An equation (or rule) can tell how to determine

the dependent variable for a specific value of the

independent variable. For example, if the value of

yis twice the value of x, the equation is

• As a table


• As a graph

FIGURE 44includes a table and graph for

relation Ffrom Example 1(a).

x

y

0

22 2

(^4) y = 2x
Graph of the relation
defined by y = 2x
FIGURE 45
Dependent Independent
variable variable

y= 2 x.

The solutions of this equation define an infinite

set of ordered pairs that can be represented by the

graph in FIGURE 45.

NOTE Another way to think of a function relation-

ship is to think of the independent variable as an input

and the dependent variable as an output. This is illus-

trated by the input-output (function) machine for the

function defined by

y= 2 x. y = 2

x

4

(Input x)

8

(Output y)

Function machine

In a function, there is exactly one value of the dependent variable, the second

component, for each value of the independent variable, the first component.