Does this look right?

[vapid sun]

Need little correction here.

[vapid sun]

You need plot it in the neighborhood of 3 not 2

[viral grail]

oh shoot

oops

[viral grail]

anything besides that?

[vapid sun]

Make sure the graph doesn't cut the asymptode

[viral grail]

how would i draw it without cutting it?

[vapid sun]

Like this. The curve shouldn't cut the asymptote

[viral grail]

than how can i get the behavior that ti wants without crossing it?

[vapid sun]

In this picture your curve (black one) cuts the asymptote (yellow one). When values tends to infinity it doesn't cut the asymptote instead it just has little space between them which denotes it tends to infinity

Same goes for - infinity

From far you see it as like it's gonna overlap but when you zoom it has little distance between them. Make it like that.

[viral grail]

so will i have more than two curves?

[vapid sun]

Yes since you already drew 2 curves. The two rectangular hyperbolas

[vapid sun]

Perfect

[viral grail]

thanks, so its ok to cross the horizontal asymptotes

[vapid sun]

No it's not okay to cross the horizontal too but this graph seems fine to me cause when you zoom it doesn't cross

The reason it doesn't cross because when you cross it. At that particular value of x the f(x) becomes 0 and no more becomes infinite. So x tends to infinite the f(x) tends to 0 goes on too

[viral grail]

so it should just be an empty circle?

[vapid sun]

Yes

[viral grail]

.solved