Just to add on a couple of images which I found online about asymptotes. Though we have not formally investigated on the properties of curves in relation with asymptotes, here are a couple of images which may help you better appreciate what asymptotes are like.
Thanks to 9gag for making Mathematics a whole lot more interesting than when I was a kid ;)
An appreciation of LOTR is needed here to understand Gandalf's role as a gatekeeper
You need to know what "Friendzoned" means here!