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    Function (mathematics) - Wikipedia

    • In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Histo… See more

    Definition

    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 … See more

    Notation

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

    Other terms

    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 spec… See more

    Specifying a function

    Given a function , by definition, to each element of the domain of the function , there is a unique element associated to it, the value of at . There are several ways to specify or describe how is related to , both explicitly an… See more

    Representing a function

    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… See more

    General properties

    This section describes general properties of functions, that are independent of specific properties of the domain and the codomain.
    There are a number of standard functions that occur frequently:
    • For … See more

    In calculus

    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 t… See more

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