The y asymptote in a function refers to the horizontal asymptote, or the horizontal line that function generally does not go through. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the x axis, or y = 0. If the degrees in the numerator and denominator are the same, then the asymptote is y = 1. If the degree in the numerator is higher than the degree of the denominator the asymptote is oblique, or a straight line. I am going to attempt to attach a graph with an asymptote of y = 0 ( the degree of the numerator is less than the degree of the denominator) and one with an oblique so you can see the difference. There are also vertical asymptotes, but that's another concept.
