Next I'll turn to the issue of horizontal or slant asymptotes. Since the degrees of the numerator and the denominator are the same (each being 2), then this rational has a non-zero (that is, a non-x-axis) horizontal asymptote, and does not have a slant asymptote.The horizontal asymptote is found by dividing the leading terms: How to Find Asymptotes & Holes. Updated April 24, 2017. By Contributor. The Graph of a Rational Function, in many cases, have one or more Horizontal Lines, that is, as the values of x tends towards Positive or Negative Infinity, the Graph of the Function approaches these Horizontal lines, getting closer and closer but never touching or even. A General Note: Removable Discontinuities of Rational Functions. A removable discontinuity occurs in the graph of a rational function at [latex]x=a[/latex] if a is a zero for a factor in the denominator that is common with a factor in the numerator.We factor the numerator and denominator and check for common factors. If we find any, we set the common factor equal to 0 and solve. The asymptote calculator takes a function and calculates all asymptotes and also graphs the function. The calculator can find horizontal, vertical, and slant asymptotes. If both polynomials are the same degree, divide the coefficients of the highest degree terms. Example: Both polynomials are 2 nd degree, so the asymptote is at ; If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote. Horizontal asymptotes are approached by the curve of a function as x goes towards infinity. Calculate their value algebraically and see graphical examples with this math lesson. My Applications of Derivatives course: To find the horizontal asymptotes of a rational fu. A horizontal asymptote is a horizontal line on a graph that the output of a function gets ever closer to, but never reaches. In more mathematical terms, a function will approach a horizontal asymptote if and only if as the input of the function grows to infinity or negative infinity, the output of the function approaches a constant value c. Symbolically, this can be represented by the two. Asymptotes are lines which are approaches closely by a certain function. Learn what an asymptote looks like and how to calculate them using algebra with this math lesson.