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, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.
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