What does the graph look like to the right?

What does the graph look like to the left?

Since there is a vertical asymptote at $x = − 5$, the limit does not exist. But we can still determine if $f(x)$ approaches $+\infty$, $−\infty$ or both. We are to determine if there is agreement among the limits as $x \rightarrow − 5$ from each side.

$\text{Test }\lim \limits_{x\rightarrow -5^{+}}f(x)=\lim \limits_{x\rightarrow -5^{+}}\frac{x-3}{x+5}=$

Test a point close to $x = −5$ but a little bit larger:

$\lim \limits_{x\rightarrow -4.9^{+}}\frac{x-3}{x+5}=\frac{(-)}{(+)}=(-)$

Therefore, $x \rightarrow −5^+, f(x) \rightarrow −\infty$

$\text{Now test }\lim \limits_{x\rightarrow -5^{-}}f(x)$

$\text{You will find }f(x)\rightarrow +\infty .$

$\text{Since }\lim \limits_{x\rightarrow -5^{+}}f(x)\neq \lim \limits_{x\rightarrow -5^{-}}f(x)$

$\lim \limits_{x\rightarrow -5}f(x)\text{ does not exist.}$

Evaluate and simplify.

Refer to hint (d).

Refer to hint (d).

Refer to hints (a) and (b).