SOLUTION: Is there any horizontal asymptotes for f(x) = (x-4)/((x^2)-4)? If so, what is it?

Question 966275: Is there any horizontal asymptotes for f(x) = (x-4)/((x^2)-4)? If so, what is it?
Answer by josgarithmetic(39631) (Show Source): You can put this solution on YOUR website!
Again? This has already been discussed AND answered. You already have this answer!

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Some expressed continued confusion:

The horizontal asymptote (if the function has one) is the UNBOUNDED behavior for the function as x tends toward either negative infinity or positive infinity. Do not focus on the function crossing this line (asymptote); just look at the what the function approaches as x goes increasing positive or increasingly negative.

As x goes unbounded to the left (meaning toward negative infinity),
the component function's highest terms become increasingly more important in the ratio of their values:

and
as x goes toward negative infinity, tends toward BUT NEVER BECOMES zero.

... Same with x going toward positive infinity, unbound toward the right.

The horizontal asymptote is .
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