In science, many functions are given by a table that gives the outputs for selected inputs. Others are given by a picture, called the graph of the function. Some functions may be described by a formula or algorithm that tells how to compute the output for a given input. There are many ways to describe or represent a function. For example, a function could associate a triangle with the number 3, a square with the number 4, and so on. Inputs and outputs need not be numbers – they can be elements of any set, for instance geometric figures. The input to a function is often called the argument and the output is often called the value. If the input is –3, then the output is 9, and we may write f(–3) = 9. The output of the function f corresponding to an input x is denoted by f( x) (read " f of x"). An example of such a relation is defined by the rule f( x) = x 2, which relates an input x to its square, which are both real numbers. In mathematics, a function is a relation between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. The property of having one output for each input is represented geometrically by the fact that each vertical line (such as the yellow line through the origin) has exactly one crossing point with the curve. The red curve is the graph of a function f in the Cartesian plane, consisting of all points with coordinates of the form ( x, f( x)).
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