In a relation, or ordered pair, the first element is called the domain of the relation.
The second element is called the range of the relation.

 

Example

Given the ordered pair (3, 6) 3 is the domain of the relation, and 6 is the range of the relation.

 The rule of a relation tells us the relationship
between the domain and the range.
 

Let's look at a relation in which the domain and the range are the same set of three numbers: (1, 2 and 3) Domain = (1,2,3) Range = (1,2,3)  The rule for this relation is :  "Odds map to 1, evens to 2 and primes to 3" This relation could be expressed in a number of ways....

\First....as a set of ordered pairs:
{(1,1), (2,2), (2,3), (3,1), (3,3)}

Next...as a table of values:
 

And also as a graph on the coordinate plane:

Now, let's take a look at a function....

 Function

A "function" is a relation in which element in the domain corresponds to one and only one element in the range.
Another way of explaining a function is that no two ordered pairs can ever have the same "x" value.