A function is a special kind of a relation because each and every element in the domain is assigned to one element in the range.
We can also say it this way:
A function is a relation where each x-value in the domain is paired, associated, matched, or mapped to a unique y-value in the range.
However, there’s a little nuisance that we always need to watch out. It is required that ALL x-values or members of the domain MUST be paired with only one y-value or member in the range.
To illustrate the point that all elements in the domain must have a corresponding y-value, take a look at the two mapping diagrams below.
- Not a Function
As you can see, this is NOT a function because there is an element in the domain, which is 6, that is not associated with any element in the range.