In mathematics a function is a relation between a given set of elements (the domain) and another set of elements (the codomain), which associates each element in the domain with exactly one element in the codomain. The elements so related can be any kind of thing (words, objects, qualities) but are typically mathematical quantities, such as real numbers.
There are many ways to represent or visualize functions: a function may be described by a formula, by a plot or graph, by an algorithm that computes it, by arrows between objects, or by a description of its properties. Sometimes, a function is described through its relationship to other functions (for example, inverse functions). In applied disciplines, functions are frequently specified by tables of values or by formulas.
In a setting where outputs of functions are numbers, functions may be added and multiplied, yielding new functions. Collections of functions with certain properties, such as continuous functions and differentiable functions, usually closed under certain operations, are called function spaces and are studied as objects in their own right, in such disciplines as real analysis and complex analysis. An important operation on functions, which distinguishes them from numbers, is composition of functions. The composite function is obtained by using the output of one function as the input of another. This operation provides the theory of functions with its most powerful structure.
In pure mathematics, functions are defined using set theory, and there are theorems that show the existence of uncountably many different functions, most of which cannot be expressed with a formula or algorithm.
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dmehling
Fri, 11 Sep 2009 19:46:52 GM
When you plug in a particular . function. into the difference quotient, what does the resulting answer mean? For example if you take the . function. of x^2 and plug it into the difference quotient you end up with the answer of 2x (I found the ...
