When Is a Relation a Function?

A relation is a function if the x-values map to only one y-value. In other words, if a relation is one-to-one or many-to-one it is a function.

How do you know if the relation is a function?

A relation is a function only if it relates each element in its domain to only one element in the range. When you graph a function, a vertical line will intersect it at only one point.

What makes a relation a function?

A function is a relation in which each input has only one output. In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y.

Sarah Jenkins

Sarah Jenkins

Senior Technology Editor & AI Specialist

Sarah Jenkins is a veteran tech journalist with over 12 years of experience covering artificial intelligence, mobile innovations, and digital ethics. Her insights have appeared in leading technology publications worldwide.