NOTE: A common mistake that students make is to think that a graph cannot cross a slant or horizontal asymptote. ... A graph CAN cross slant and horizontal asymptotes (sometimes more than once). It's those vertical asymptote critters that a graph cannot cross.

How many times can a function cross a horizontal asymptote?

approaches is called a horizontal asymptote . crosses its horizontal asymptote y=0 infinitely many times.

Can a function cross a vertical asymptote?

Note that your graph can cross over a horizontal or oblique asymptote, but it can NEVER cross over a vertical asymptote.