What about the middle neighborhood?
We'll need to quickie plot two points... Try it before going on.
NOTE: A common mistake that students make is to think that a graph cannot cross a slant or horizontal asymptote. This is not the case! A graph CAN cross slant and horizontal asymptotes (sometimes more than once). It's those vertical asymptote critters that a graph cannot cross. This is because these are the bad spots in the domain.