In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by , where f is the function.
More precisely, given a function , the domain of f is X. Note that in modern mathematical language, the domain is part of the definition of a function rather than a property of it.
In the special case that X and Y are both subsets of , the function f can be graphed in the Cartesian coordinate system. In this case, the domain is represented on the x-axis of the graph, as the projection of the graph of the function onto the x-axis.
For a function , the set Y is called the codomain, and the set of values attained by the function (which is a subset of Y) is called its range or image.
Any function can be restricted to a subset of its domain. The restriction of to , where , is written as .