use f(x)= x/ absolute value of x, to find lim x infinity, lim x - infinity, and all horizontal asymptotes??

Question

use f(x)= x/ absolute value of x,  to find lim x> infinity, lim x> - infinity, and all horizontal asymptotes??

anonymous · Answer

@CarlosGP, would lim f(x) x>- infinity = -1 ?
and lim f(x) x->infinity = 1 ??

anonymous · Answer

@Hero ?

hero · Answer

Actually, for this one, it is tricky.

hero · Answer

Simply because..

$$\frac{x}{x} = 1$$ and $$-\frac{x}{x} = -1$$

hero · Answer

So basically, when that happens, it means there's no horizontal asymptote.

hero · Answer

If yo graph it, you'll see two lines where f(x) = 1 and f(x) = -1 graphically

hero · Answer

But there's no horizontal asymptote

anonymous · Answer

hmmm, yeah I guess I can see why there wouldn't be a horizontal asymptote !

anonymous · Answer

(:

anonymous · Answer

think you could help me out with 2 more? D: (:

hero · Answer

That's the reason why I try to simplify these first before attempting to find asymptotes.

anonymous · Answer

i wasn't taught how to simplify them to find the asymptotes, we just graph :o

anonymous · Answer

find the verticle asymptote of f(x)= 1/(x^2 -4)

anonymous · Answer

and describe the behavior of f(x) to the left and right of each asymptote