Define a function in terms of it's input and output

technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

This means that if the object x is in the set of inputs (called the domain) then a function f will map the object x to exactly one object f (x) in the set of possible outputs (called the codomain).

The notion of a function is easily understood using the metaphor of a function machine that takes in an object for its input and, based on that input, spits out another object as its output.

A function is more formally defined given a set of inputs X (domain) and a set of possible outputs Y (codomain) as a set of ordered pairs.