Condition for a Relation to Be a Function

Every element of \(A\) must appear as the first element in exactly one ordered pair

Explanation

A relation is a function if and only if: (1) every element of the domain \(A\) is associated with some element of \(B\) (total definition), and (2) no element of \(A\) is associated with more than one element of \(B\) (uniqueness). Equivalently, in the set of ordered pairs, each element of \(A\) appears exactly once as a first component. Elements of \(B\) may appear zero, one, or multiple times as second components.