Absolute value functions are continuous. Square root functions are continous for positive inputs.
We can estimate the left and right hand limits by choosing points close to \(-3\)
Left handed limit
$$ \lim\limits_{x\to -3^-} \approx f(-3.01) $$
$$ f(-3.01) = \sqrt{|-3.01+3|} $$
$$ = \sqrt{.01} $$
Right handed limit
$$ \lim\limits_{x\to -3^+} \approx f(-2.99) $$
$$ f(-2.99) = \sqrt{|-2.99+3|} $$
$$ = \sqrt{.01} $$
The limit exists because the left and right handed limits are equal. The limit appears to be approaching \(0\).
Similarly, \(f\) is continuous because \(f(-3)=0\) which equals the limit.
Absolute value functions are not differentiable at their vertex.