$f(x)=\{\begin{array}{ccc}x-8& if& x0\\ x^2+x-8& if& x>0\end{array}$

Is f continuous at $0?$ Select the correct choice below and, if necessary, fill in the answer boxes to complete your answer choice.

A$.$ Yes, because $f(0)=$ and $\underset{x0}{lim}f(x)=$ and $f(0)=\underset{x0}{lim}f(x)$

B$.$ No$,$ because $f(0)$ does not exist

C$.$ Yes, because $f(0)$ and $\underset{x0}{lim}f(x)$ exist.

D$.$ No$,$ because $f(0)=$ and $\underset{x0}{lim}f(x)=$ and $f(0)\underset{x0}{lim}f(x)$