Let $f(x)= \left\{\begin{matrix}|x|+3& if& x ≤-3\\ -2x& if& -3<x<3\\6x+2& if& x≥3\end{matrix}\right.$, then which of the following is true?

$f(x)$ is discontinuous at $x = 3$

The correct answer is Option (4) → $f(x)$ is discontinuous at $x = 3$

$f(x)=|x|+3$ for $x\le -3$

$f(x)=-2x$ for $-3

$f(x)=6x+2$ for $x\ge 3$

At $x=-3$: $f(-3^-)=|-3|+3=6,\ \ f(-3^+)= -2(-3)=6,\ \ f(-3)=6 \Rightarrow$ continuous.

At $x=3$: $f(3^-)= -2(3)=-6,\ \ f(3^+)=6(3)+2=20,\ \ f(3)=20 \Rightarrow$ discontinuous.

Answer: $f(x)$ is discontinuous at $x=3$.