There are three rules that horizontal asymptotes follow depending on the degree of the polynomials involved in the rational expression. Before we begin, let's define our function like this:[br]horizontal asymptote[br][br]Our function has a polynomial of degree n on top and a polynomial of degree m on the bottom. Our horizontal asymptote rules are based on these degrees.[br]1. When n is less than m, the horizontal asymptote is y = 0 or the x-axis.[br]2. When n is equal to m, then the horizontal asymptote is equal to y = a/b, the leading coefficient of numerator/the leading coeffcient of denominator.[br]3. When n is greater than m, there is no horizontal asymptote.[br][br]The degrees of the polynomials in the function determine whether there is a horizontal asymptote and where it will be. [br][br]Vertical asymptotes are straight lines of the equation x = a, toward which a function r(x) approaches infinitesimally closely, but never reaches the line, as r(x) increases without bound.[br]Let's see how we can use these rules to figure out horizontal asymptotes and vertical Asymptote. [br][br]Steps:[br]1. Input a expression for f(x), input a expression for g(x). try all three cases. Guess the Asymptote(s)[br]2. check the Horizontal Asymptote box to see if you have correct answer[br]3. check the Vertical Asymptote.