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

The correct answer is Option (1) → A continuous function

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

and,

$\lim\limits_{x \to 0}\frac{x}{|x|}=\lim\limits_{h \to 0}\frac{h}{-h}=-1$

$\lim\limits_{h \to 0^+}-1=-1$

and,

$f(0)=-1$

∴ it is a continuous function.