How might an asymptote be useful?
A function describes a relationship between two sets such that for every input there is exactly one output. The graph of the function is a visual representation of the relation decribed by the function rule. In some cases the rule that describes the function relationship can be quite complicated and time consuming to evaluate but if a linear asymptote exists, then it can be used to approximate the output of the function without going through the complicated function definition. This will be shown through the examples below. There are three situations in which we will have linear end behavior asymptotes. (i.) If the degree of the numerator is less than the degree of the denominator. (ii.) If the degree of the numerator equals the degree of the denominator. (iii.) If the degree of the numerator is one more than the degree of the denominator. While there are short-cuts to find the end behavior asymptote in two of these three cases, they all derive from the same procedure. I will first sum
