A function is a special mathematical relationship in which each input has exactly one unique output. It is like an input-output machine. It has 3 parts: the input, the relationship or rule, and the output. Every input relates to some output in a function, and one input cannot produce 2 different outputs in the same function. Each input has a unique output. Given a set of ordered pairs, an x-coordinate will never appear with more than one unique y-coordinate. Given a graph, a vertical line when drawn will never cross more than one value. Given a table, the x-value/input will never appear with more than one unique y-value/output.

How do your figure out if a relation is a function? Video

Khan Academy’s Recognizing Functions

Vertical Line Test Video (student created video)