Define a function $f:\mathbb{R}\rightarrow \mathbb{R}$ as $f(x)=\begin{cases}\frac{x}{|x|}& \text{if}\hspace{.2cm} x <0\\ -1 & \text{otherwise} \end{cases}$. Then $f$ is

A continuous function Discontinuous at 0 Continuous everywhere except 0 None of the above

A continuous function

$f$ is continuous at $x=0$ because $\lim_{x \to 0}f(x)=-1=f(0)$ and it is continuous everywhere else.