Determining Whether a Relation Is a Function

Determining Whether a Relation Is a Function

Review

A relation is an equation in which one variable depends on the value of another variable.  The variables are x (domain) and y (range).

 

Function

is a special kind of relation in which every element in the domain is paired with exactly one element in the range. 

Important!

the difference between a relation and a function is that in a relation a domain (x) can be related to more than one value of range (y). In the function a domain (x) can be related only to one value. 

This is a relation

but not a function! We can see that range (y) can be paired with more than one domain (x).

This is both a relation and a function!

We can see that each domain (x) can be paired with only one range (y).

Let's practice

This is not a function because both domains 3 and 4 are paired with range 5.

This is a function

because each domain (x) is paired with only one range (y).