> [!Definition] Definition (Real valued function of several real variables) > A [[Function|function]] $f:U \subset \mathbb{R}^{n} \to \mathbb{R}$ for some $n=1,3,4,\dots$ > > [!info] > Note that for $n=1$, $f$ is a [[Real Function]]. # Properties - Represents a [[Algebraic Surface]] in $\mathbb{R}^{n+1}$. - If $n\leq 2$, the real-valued function can be visualised in $\mathbb{R}^{3}$ using a [[Graph of functions on real n-space|graph]]. - If $n=2,3$ the real-valued function can also be visualised using [[Level Sets of Real-Valued Function of Several Real Variables|contour plots]]. - See [[Fréchet Differentiation]]. - See [[Fréchet Differentiation]]. - See [[Fréchet Differentiation]] & [[Normal Vector of Surface]]. - See [[Critical Point of Real-Valued Function on Real 2-Space]]. # Examples