Graph

The graph of a function $f:X\to Y$ is the subset $f=\{(x,f(x)):x\in X\}\subset X\times Y$

N-Dim Graph

A graph for function $f:X\subset {\mathbb{R}}^n\to \mathbb{R}$ is a subset of ${\mathbb{R}}^{n+1}$. $graphf=\{(x_1,..,x_n,f(x_1,\dots ,x_n))\in {\mathbb{R}}^{n+1}|(x_1,\dots ,x_n)\in X\}$

Examples

• The graph of $f(x)=x^2$ is a subset of $\mathbb{R}\times \mathbb{R}={\mathbb{R}}^2$
• The graph of $g(x,y)=x^2+y^2+1$ is a subset of ${\mathbb{R}}^2\times \mathbb{R}={\mathbb{R}}^3$