## Calculus (3rd Edition)

$f(x)$ is discontinuous at $x=1$. The graph is right-continuous at $x=1$
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 $x=1$.