How do you know where and when the graph crosses the horizontal asymptote?

The horizontal asymptote is the line which the curve approaches to cross but never crosses the boundary. The horizontal asymptote can be identified when the exponent in the denominator of the function is larger than the exponent in the numerator. If not, no horizontal asymptote exists. WHen there is, we equate the denominator to zero and get x

Bi’m pretty sure hope it works