Graph of example function,

A function, in mathematics, associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can also be elements from any given set. An example of a function is f(x) = 2x, a function which associates with every number the number twice as large. Thus 5 is associated with 10, and this is written f (5) = 10.

The input to a function need not be a number, it can be any well defined object. For example, a function might associate the letter A with the number 1, the letter B with the number 2, and so on. There are many ways to describe or represent a function, such as a formula or algorithm that computes the output for a given input, a graph that gives a picture of the function, or a table of values that gives the output for certain specified inputs. Tables of values are especially common in statistics, science, and engineering.

The set of all inputs to a particular function is called the domain. In modern mathematics functions are normally defined to have a codomain associated with them which is some fixed set which includes all possible outputs, for instance real valued functions have a codomain which includes all the real numbers even though each particular real valued function may not include every real number as an output. The set of all the ordered pairs or inputs and outputs (x, f(x)) of a function is called its graph. A common way to define a function is as the triple (domain, codomain, graph), that is as the input set, the possible outputs and the mapping for each input to its output.

The set of all outputs of a particular function is called its image. The word range is used in some texts to refer to the image and in others to the codomain, in particular in computing it often refers to the codomain. The domain and codomain are often "understood". Thus for the example given above, f(x) = 2x, the domain and codomain were not stated explicitly. They might both be the set of all real numbers, but they might also be the set of integers. If the domain is the set of integers, then image consists of just the even integers. (Our solved example in mathguru.com uses this concept)

http://en.wikipedia.org/wiki/Function_(mathematics)

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