Relations approximated by continuous functions

Let $X$ be a Tychonoff space, let $C(X)$ be the space of all continuous real-valued functions defined on $X$ and let $CL(X \times R)$ be the hyperspace of all nonempty closed subsets of $X\times R$. We prove the following result. Let $X$ be a locally connected, countably paracompact, normal $q$-space without isolated points, and let $F \in CL(X \times R)$. Then $F$ is in the closure of $C(X)$ in $CL(X \times R)$ with the locally finite topology if and only if $F$is the graph of a cusco map. Some results concerning an approximation in the Vietoris topology are also given.