I thought that horizontal asymptotes were asymptotes and now I'm hearing that they can be crossed... Is this true? If so, why and how? Okay, wait a second, I mean horizontal asymptotes. According to: http://www.purplemath.com/modules/asymtote2.htm "As I mentioned before, it is common and perfectly okay to cross a horizontal asymptote. It's the verticals that you're not allowed to touch." In what cases are horizontal asymptotes crossed? I've never encountered such a thing before... at least I think. Please give me a simple equation or something. Thanks in advance!