We show that for each positive integer $k$ there is a sequence $F_n:\Bbb{R}^k \rightarrow\Bbb{R}$ of {t continuous} functions which represents via point-wise limits {t arbitrary} functions $G\:X^k\rightarrow \Bbb{R}$ defined on domains $X\subseteq \Bbb{R}$ of sizes not exceeding a standard cardinal characteristic of the continuum.