Definition of a Function. A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair. Okay, that is a mouth full.herefore this relation is a function. In order to really get a feel for what the definition of a function is telling us we should probably also check out an example of a relation that is not a function. Example 2 The following relation is not a function. Solution. Don’t worry about where this relation came from.