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Graph of a Function

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Let $ f = f(x_1, \ldots , x_n)$ be a real function. The graph of $ f$ is the subset of $ \mathbb{R}^{n+1} $ defined by

$\displaystyle \{ (x_1, \ldots ,x_{n+1}) \in \mathbb{R}^{n+1} ; x_{n+1} = f(x_1, \ldots ,x_n) \} .$

In particular, if $ f = f(x,y)$ is a function of two variables, then the graph of $ f$ consists of all points $ (x,y,z)$ in space such that $ f$ is defined for $ (x,y)$ and $ z = f(x,y) .$

see also:

  automatically generated 4/ 7/2005