Suppose you wish to find the asymptotes of the following:

2x/(3x + 2)

To find the vertical asymptote, find where the denominator is undefined for x. Set the denominator equal to zero.

3x + 2 = 0

x = -2/3

Therefore the vertical asymptote is the line x = -2/3

To find the horizontal asymptote, divide the coefficients of the x term (numerator/denominator). Notice the coefficients are 2 and 3.

The horizontal aymptote is the line y = 2/3.


The graph will approach but never touch the asymptotes.