Consider the following function:

$f(x)=\{\begin{array}{ccc}x-2,& if& x-1\\ 3x,& if& -10\end{array}$

a$.$ Is $f(x)$ continuous at $x=0?$

A$.$ No

B$.$ Yes

b$.$ Is $f(x)$ differentiable at $x=0?$

A$.$ No

B$.$ Yes

c$.$ Suppose a different function $g(x)$ is not differentiable at $x=a.$ Does this guarantee that $g(x)$ is also not continuous at $x=a?$

A$.$ No

B$.$ Yes