The graph below shows $f(x).$ Note that:

The graph of $f(x)$ has a sharp corner at $x=9$ and nowhere else.

At $x=4$ the function has a vertical asymptote.

$f(x)$ does not intersect the $x-$axis at $x=11,$ instead there is a horizontal asymptote.

Let $f^{\text{'}}(x)$ be this function's derivative.

$($a$)$ Find $\underset{x{4}^{-}}{lim}f(x)$

$($b$)$ Find $\underset{x{3}^{+}}{lim}f(x)$

$($c$)$ List all values of $x$ where $f(x)$ is not continuous.

$($d$)$ List all values of $x$ where $f(x)$ is not differentiable.