Question

What is the best way to tell if function approaches positive or negative ∞?

Answer 1

Look at the degree of the highest-power term

Explanation:

The question you asked is "how do you tell?" You look at the degree of the controlling term. Usually, that is the term with the highest power.

Here, as you approach x=4 (from either direction), the denominator approaches zero. The term is squared, so is always positive. That means the quotient is always positive, and the limit will always be +∞.

If the term had an odd degree (cubed, for example), then its sign would depend on the approach direction.

_____

A graphing calculator can help you get a feel for how this works.