function

Also known as mathematical function, single-valued function, total function, map, application, mapping

association of a single output to each input

AI overview

A function is a relationship where each input is paired with exactly one output. Functions matter because they're a fundamental way to describe how things depend on each other—whether in mathematics, science, or everyday situations like how your paycheck depends on your hours worked.

AI-generated from the Wikipedia summary — may contain errors.

Wikidata facts

Subclass of: generalized function
Image: Exp re.png

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studied by: mathematics
opposite of: multivalued function
maintained by WikiProject: WikiProject Mathematics
Commons category: Functions (mathematics)
topic's main category: Category:Functions and mappings
has list: list of mathematical functions
has characteristic: arity
on focus list of Wikimedia project: Wikipedia:Vital articles/Level/4
different from: position
described at URL: www.khanacademy.org/math/linear-algebra/matrix-transformations/linear-transformations/v/a-more-formal-understanding-of-functions

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Encyclopedic overview

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. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly increased the possible applications of the concept.

Excerpted from Wikipedia’s “function” article, available under the CC BY-SA 4.0 licence.