A function f from a set X to a set Y is an assignment of one element of Y to each element of X. The set X is called the domain of the function and the set Y is called the See more

There are various standard ways for denoting functions. The most commonly used notation is functional notation, which is the first notation described below.
Functional notation
The functional notation requires that a name is given to … See more

Given a function $${\displaystyle f}$$, by definition, to each element $${\displaystyle x}$$ of the domain of the function $${\displaystyle f}$$, … See more

This section describes general properties of functions, that are independent of specific properties of the domain and the codomain. See more

A function may also be called a map or a mapping, but some authors make a distinction between the term "map" and "function". For example, the term "map" is often reserved for a "function" with some sort of special structure (e.g. maps of manifolds See more

A graph is commonly used to give an intuitive picture of a function. As an example of how a graph helps to understand a function, it is easy to see from its graph whether a function is increasing or decreasing. Some functions may also be … See more

The idea of function, starting in the 17th century, was fundamental to the new infinitesimal calculus. At that time, only real-valued functions of a real variable were considered, and all functions were assumed to be smooth. But the definition was soon extended … See more