Question

Give an example of a rational function that has no horizontal asymptote and a vertical asymptote at
x = 1.

Answer 1

No horizontal asymptote? that means your function does not approach any particular limit as x increases from left to right. How might that be possible? What about a slant asymptote, in which the graph gets closer and closer to a slanting line as x increases without bound? What property of your function would lead to a vertical asymptote at x=1?

Answer 2

I have no idea