  The \emph{metric dimension} of a graph $G$, denoted by $\dim(G)$, is the
minimum number of vertices such that each vertex is uniquely determined by its
distances to the chosen vertices. Let $G_1$ and $G_2$ be disjoint copies of a
graph $G$ and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a
\emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$
and the edge set $E=E(G_1) \cup E(G_2) \cup \{uv \mid v=f(u)\}$. We study how
metric dimension behaves in passing from $G$ to $C(G,f)$ by first showing that
$2 \le \dim(C(G, f)) \le 2n-3$, if $G$ is a connected graph of order $n \ge 3$
and $f$ is any function. We further investigate the metric dimension of
functigraphs on complete graphs and on cycles.
