\begin{definition}[Definition:Graph of Real Function]
Let $U \subseteq \R^n$ be an open subset of $n$-dimensional Euclidean space.
Let $f : U \to \R^k$ be a real function.
The '''graph''' $\map \Gamma f$ of the function $f$ is the subset of $\R^n \times \R^k$ such that:
:$\map \Gamma f = \set {\tuple {x, y} \in \R^n \times \R^k: x \in U \subseteq \R^n : \map f x = y}$
where $\times$ denotes the Cartesian product.
\end{definition}