What Is a Method for Finding Vertical and Horizontal Asymptotes?

If you are given a rational function, you can find the vertical asymptote by setting the denominator to zero and solving the equation. Find the horizontal asymptote by dividing the leading terms in the function.

A vertical asymptote is a line that a curve approaches but does not cross. The distance between the curve and the line approaches zero as they tend to infinity. The equation of the vertical asymptote is found by determining the root of the denominator. When finding the vertical asymptote, the numerator is ignored. Separate the denominator from the rational function, and set the denominator equal to zero. Solving this equation yields the vertical asymptote.

A horizontal asymptote is a line to the far left or right of the curve. To find the horizontal asymptote, one should determine the degree of both the numerator and denominator from the original function. If the degrees are the same, simply divide the first term of the numerator by the first term of the denominator. This gives the y-value of the horizontal asymptote. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the x-axis. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.