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Mathematics-Online lexicon:

Functions

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A function

$\displaystyle f: D\rightarrow \mathbb{R}\,,\quad x \mapsto f(x) $

associates each argument $ x$ in the domain $ D \subseteq \mathbb{R}$ to a value $ f(x)$ in the range $ W \subseteq\mathbb{R}$ .

The graph of $ f$ consists of all pairs $ (x,y)$ with $ y=f(x)$ .

\includegraphics[bb=140 533 337 718,clip,width=.45\linewidth]{Def_Bereich}

As the illustration shows, domain (colored in light-grey) and range (colored in dark-grey) simply are the graph's projections onto the $ x$ - and $ y$ -axis respectively.

(Authors: Höllig/Hörner/Knödler/Abele)

Examples:

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  automatically generated 4/ 8/2008