Consider the following function.

$g(x)=\frac{x}{x-3}$

Find $g^{\text{'}}(x)$ and $g^{\text{'}\text{'}}(x).$

$g^{\text{'}}(x)=$

$g^{\text{'}\text{'}}(x)=$

Determine the domain of $g.($Enter your answer using interval notation.$)$

$$

Find the $x-$ and $y-$intercepts of $g.($Enter your answers as comma$-$separated lists. If an answer does not exist, $$nter DNE.$)$

$x-$intercepts $,x=$

$y-$intercepts $,y=$

Determine the behavior of $g$ for large absolute values of $x.($If the limit is infinite, enter $\text{'}{}^{\text{'}}$ or $\text{'}-{}^{\text{'}},$ as appropriate. If the limit does not otherwise exist, enter DNE.$)$

Find the horizontal and vertical asymptotes of the graph of $g.($If an answer does not exist, enter DNE.$)$

horizontal asymptote $,y=$

vertical asymptote $,x=$