Explain why the function is discontinuous at the given number $a.($Select all that apply.$)$

$f(x)=\frac{1}{x+4},a=-4$

$\backslash$table$[[\underset{x-4^{+}}{lim}f(x)$ and $\underset{x-4^{-}}{lim}f(x)$ are not finite, and are not equal.$],[f(-4)$ and $\underset{x-4}{lim}f(x)$ are finite, but are not equal.$],[\underset{x-4}{lim}f(x)$ does not exist.$],[f(-4)$ is undefined.$],[$none of the above$]]$

Sketch the graph of the function.

Explain, using these theorems, why the function is continuous at every number in its domain.

$g(v)=\frac{6v-1}{v^2+3v-54}$

$g(v)$ is a trigonometric, so it is continuous at every number in its domain.

$g(v)$ is a polynomial, so it is continuous at every number in its domain.

$g(v)$ is a rational function, so it is continuous at every number in its domain.

$g(v)$ is an exponential function, so it is continuous at every number in its domain.

$g(v)$ is not continuous at every number in its domain.

State the domain. $($Enter your answer using interval notation.$)$