Answer
$$ lim(x\rightarrow \infty)=\infty $$
$$ lim(x\rightarrow -\infty)=\text{does not exist}$$
Work Step by Step
We look at the term of the highest degree for the polynomial. Doing this, we see that this is a square root function with a positive coefficient. Thus:
$$ lim(x\rightarrow \infty)=\infty $$
$$ lim(x\rightarrow -\infty)=\text{does not exist}$$