6th Grade Math Textbook, Fundamentals

 &KDSWHU

13-4

Key Concept

Functions

A function is a set of ordered pairs, (x, y), in

which there is only one y-value for each x-value.

Type of Relation Description Example

One to one For each input value, there is only

one output value. This one-to-one

type of relation is called a function.

The amount earned depends on

the amount of time worked.

(work 1 hour, earn $20)

One to many One input value corresponds to

many output values.

This relation is nota function.

One date corresponds to many

people’s birthdays.

(date, person’s birthday)

Many to one Many input values correspond to

the same output value.

This relation is a function.

Several students may have the

same grade.

(student, test grade)

Many to many Many input values correspond to

many output values.

This relation is not a function.

Many teachers can have the same

student, and many students can

have the same teacher.

(teacher, student)

Relations and Functions

Objective To identify the domain and range of a relation• To identify a given relation as a

function or not a function• To write an equation to represent a function from a table of values

In 1963, there were only 417 male-female pairs of bald eagles
in the United States. Since then, the bald eagle population
has grown. In 1999, the bald eagle was removed from the list
of endangered and threatened species. The table below at the
right shows the increase in the number of bald eagle pairs
since 1996.

The data in the table demonstrate a relation. A

is a set of ordered pairs that associates two quantities

in a specific order. In this case, the relation is the

ordered pairs, (x, y), that associate a year with a number

of pairs of bald eagles.

A relation consists of a domainand a range. The

is the set of , or x-values, in the ordered pairs.

The is the set of , or y-values, in the

ordered pairs.

The domain is {1996, 1998, 2000, 2002, 2004, 2006}.

The range (in thousands) is {5.1, 5.7, 6.5, 6.7, 7.0, 9.8}.

There are different types of relations.

range output values

input values

domain

relation

Year Number of Bald Eagle Pairs (thousands)

1996 5.1

1998 5.7

2000 6.5

2002 6.7

2004 7. 0

2006 9.8