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

Horizontal asymptotes designate range values a graph approaches as the domain continues to infinity or negative infinity. Sesmoid functions have two horizontal asymptotes, but are beyond the scope of introductory calculus.

To find a horizontal asymptote, the index (highest exponent wuth a variable base) of the numerator and denominator must be equal, or the denominator must have a higher index than the numerator.

If the index of the denometer has a higher value than the numerator, then there is a horizontal asymptote y=0.

If the index of the numerator and demoninator are the same, simply divide the leading coefficient of the numerator by the leading coefficient of the denometer to obtain horizontal asymptote y=quotient.

Vertical asymptotes designate where the range approaches infinity or negative infinity as the domain approaches a value.

To find a vertical asymptote, find all zeroes in the denominator. If the numerator is not divisable by that zero, then there is a vertical asymptote x=root as long as no absolute values are involved

Example: find the horizontal and vertical asymptotes of the function y=1/x.

Answer: Since the index of the denominator is higher than the index of the numerator, there is a horizontal asymptote y=0. Since zero does not factor out of the numerator, there is a vertical asymptote x=0