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function, in mathematics, a relation *f* that assigns to each member *x* of some set *X* a corresponding member *y* of some set *Y*; *y* is said to be a function of *x,* usually denoted *f*(*x*) (read "*f* of *x* "). In the equation *y*=*f*(*x*), *x* is called the independent variable and *y* the dependent variable. In practice, *X* and *Y* will most often be sets of numbers, vectors, points of some geometric object, or the like. For example, *X* might be a solid body and *f*(*x*) the temperature at the point *x* in *X*; in this case, *Y* will be a set of numbers. The formula *A*=π*r* ^{2} expresses the area of a circle as a function of its radius. A function *f* is often described in terms of its graph, which consists of all points (*x,**y*) in the plane such that *y*=*f*(*x*). Although a function *f* assigns a unique *y* to each *x,* several *x* 's may yield the same *y* ; e.g., if *y*=*f*(*x*)=*x* ^{2} (*x* is a number), then *f*(2)=*f*(-2). If this never occurs, then *f* is called a one-to-one, or injective, function.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

Function may refer to:

- Function (biology), explaining why a feature survived selection
- Function (mathematics), an abstract entity that associates an input to a corresponding output according to some rule
- Function (engineering), related to the utility/goal of a property
- Function (computer science), or subroutine, a portion of code within a larger program, performs a specific task
- Function object, or functor or functionoid, a concept of object-oriented programming
- Grammatical function, in language studies, the purpose of a word or phrase in a sentence
- Diatonic function describes a music term
- A formal event such as a party or meeting

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Last updated on Wednesday September 10, 2008 at 15:07:28 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Wednesday September 10, 2008 at 15:07:28 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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