A mathematical relation is a mapping from a set of input values, called the domain, to a set of output values, called the range. A relation can also be described as a set of input-output pairs.

Relations in general have no further restrictions than mapping domain elements to range elements. By adding the restriction that each input value maps to exactly one output value, we define a particularly useful type of relation, called a function.

Functions are usually written using a particular notation called function notation: for a function f when x is a member of the domain, the symbol f\left(x\right) denotes the corresponding member of the range.

To evaluate a function at a point is to calculate the output value at a particular input value.

Worked examples