Asymptote dilemma

[sajib_mostofa]

I was trying to graph the function and I assumed that it had a horizontal asymptote of but when I graphed it on the calculator, the parabolic part of the graph actually crosses this asymptote but the ends of the graph does not. So my question is, at the point where it does cross the asymptote, should there be an open circle? Or have I made a mistake from the beginning by assuming there is a horizontal asymptote?

[Phy124]

If the distance between a function and a line approaches zero as they tend to infinity then the line is an asymptote to that function.

So you are correct, the line is in fact an asymptote to the function .

The asymptote is simply represented as you would if the function did not cross the line, no open circles or other additions are needed. If the graph illustrated discontinuity then open circles would be used.

Additionally, a function can cross both horizontal and diagonal asymptotes, however not vertical asymptotes (AFAIK)

[sajib_mostofa]

Cheers for the reply