Find all points of discontinuity of $f$,where $f$ is defined by $f(x) = \begin{cases} \frac{x}{|x|}, & \text{if } x < 0 \\ -1, & \text{if } x \ge 0 \end{cases}$. Is $f$ a continuous function?

(D) The given function is $f(x) = \begin{cases} \frac{x}{|x|}, & \text{if } x < 0 \\ -1, & \text{if } x \ge 0 \end{cases}$.
For $x < 0$,we have $|x| = -x$. Therefore,for $x < 0$,$f(x) = \frac{x}{-x} = -1$.
Thus,the function can be written as $f(x) = -1$ for all $x \in \mathbb{R}$.
Let $c$ be any real number. Then,$\lim_{x \to c} f(x) = \lim_{x \to c} (-1) = -1$.
Also,$f(c) = -1$ for any $c \in \mathbb{R}$.
Since $\lim_{x \to c} f(x) = f(c)$ for all $c \in \mathbb{R}$,the function $f(x)$ is continuous everywhere.
Hence,the function has no points of discontinuity.