Asymptotic+and+unbounded+behavior+(vertical+and+horizontal+asymptotes)

To find a vertical asymptote, one must set the denominator equal to zero. This is because the function would not be defined since one cannot divide by zero. If the function is not in rational form, then there are no vertical asymptotes. Ex: (x+4)/(x+7) To find the vertical asymptote: x+7=0 x=-7 (there is a vertical asymptote at x=-7)

When looking for horizontal asymptotes, one must only be concerned with the largest exponents of x in both the numerator and the denominator. If the exponent in the denominator is larger, then there is a horizontal asymptote at y=0 (the x-axis). Ex: (2x+5)/3x^2 If the exponent in the numerator is larger, then there is no horizontal asymptote. Ex: (2x+9)/3 If the exponents are equal on both the denominator and numerator, then take the constant of the denominator over the numerator. Ex: 3x/4x Horizontal asymptote is at x=3/4