## Calculus (3rd Edition)

$f(x)$ is neither left nor right continuous at $x=2$.
Given $$f(x)=\left\{\begin{array}{ll} {\dfrac{x^{2}-3 x+2}{|x-2|}} & {x \neq 2} \\ {0} & {x=2} \end{array}\right.$$ From the figure, $$\lim _{x \rightarrow 2^{-}} f(x) \neq \lim _{x \rightarrow 2^{-}} f(x) \neq f(2)$$ Then $f(x)$ is neither left nor right continuous at $x=2$ (there is a jump discontinuity at $x=2$).