Answer
$f(x)$ is discontinuous at $x=1$. The graph is right-continuous at $x=1$
Work Step by Step
Given $$
f(x)=\left\{\begin{array}{ll}
{x+1} & {\text { for } x<1} \\
{\dfrac{1}{x}} & {\text { for } x \geq 1}
\end{array}\right.
$$
From the graph, we see that $f(x)$ has a discontinuity at $x=1$.
Since $\lim _{x \rightarrow 1+} f(x)=f(1),$ then $f(x)$ is right-continuous at $x=1$.
