Answer
$f(1)=1$
Work Step by Step
Normally, by tracing the graph, we would get an other value for $f(1)$, as the limit of $\lim\limits_{x \to \ 1}f(x)$ equals to $0$.
However, the point of $f(1)$ is defined by the blue dot on the graph, where $x=1$.
Therefore, according to the graph, the value of $f(1)=1$.