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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 r2 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 ) = x2 ( 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, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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