Question

The graph of $f\left(x\right)$ is given below. Based on this graph determine where the function is discontinuous.

Answer 1

First consider the point $x=-4$. At this point

$\underset{x\to -4^{-}}{lim}f\left(x\right)[=3]\ne \underset{x\to -4^{+}}{lim}f\left(x\right)[=-2]$.

So, function is discontinuous at $x=-4$.

Similarly,consider the point $x=2$. At this point

$\underset{x\to 2^{-}}{lim}f\left(x\right)[=-1]\ne \underset{x\to 2^{+}}{lim}f\left(x\right)[=5]$.

So, function is discontinuous at $x=2$.

Now, consider the point $x=4$. At this point

$\underset{x\to 4^{-}}{lim}f\left(x\right)[=2]=\underset{x\to 4^{+}}{lim}f\left(x\right)[=2]$.

But $f\left(4\right)$ doesn't exists.

So, again function is discontinuous at $x=4$.