Function (mathematics)
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Partial plot of a function f. Each real number x is associated with the number f(x) = x3 − 9x.In mathematics, a function relates each of its inputs to exactly one output. A standard notation for the output of the function f with the input x is f(x). The set of all inputs that a function accepts is called the domain of the function. The set of all outputs is called the range.
For example, the expression f(x) = x2 describes a function, f, that relates each input, x, with one output, x2. Thus, an input of 3 is related to an output of 9. Once a function, f, has been defined, we can write, for example, f(4) = 16.
It is a usual practice in mathematics to introduce functions with temporary names like f; in the next paragraph we might define f(x) = 2x+1, and then f(4) = 9. When a name for the function is not needed, often the form y=x2 is used.
If we use a function often, we may give it a permanent name as, for example,
.
The essential property of a function is that for each input there must be one unique output. Thus, for example,
does not define a function, because it may have two outputs. The square roots of 9 are 3 and −3, for example. To make the square root a function, we must specify which square root to choose. The definition
,
for any non-negative input chooses the non-negative square root as an output.
A function need not involve numbers. An example of a function that does not use numbers is the function that assigns to each nation its current capital. In this case Capital(France) = Paris.
A more precise, but still informal definition follows. Let A and B be sets. A function from A to B is determined by any association of a unique element of B with each element of A. The set A is called the domain of the function; the set B is called the codomain.
In some contexts, such as lambda calculus, the function notion may be taken as primitive rather than defined in terms of set theory.
In most mathematical fields, the terms map, mapping, and transformation are often synonymous with function. However, in some contexts they may have a more specialized meaning. A map is usually a (total) function as defined here, especially for authors using function as synonym for partial functions with a domain (of definition) not necessarily containing all points of the source or "departure set". (For them, f:R→R; x↦1/x is a function with domain R\{0}.) A transformation most often refers to a map from a set into itself, as it is the case for geometric symmetry operations, for instance.
2006-10-26 10:04:39
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answer #1
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answered by shortys_75j 2
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If you only want an EXAMPLE of use of a function in internet or newspapers... it´s simple. Look in a financial page, as http://www.nasdaq.com and you´ll find big, in front of you a nice, big graphic function of stock transactions.
Also, if you want to buy shoes in an international shop, you should find a nice table function, with shoes sizes conversions as in http://www.columbia.edu/~zz2111/shoesizeconversion.htm
And... almost every web page where they let you introduce a variable, then click a button... is a FUNCTION! The google search is also a function. Now...you only have to chose what seems to you a good example.
Bye
2006-10-26 10:27:13
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answer #2
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answered by marcusdumitru 1
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