Curvilinear Asymptotes

[beth22]

In terms of rational functions, what happens if the degree of the numerator is two greater than the degree of the denominator? 3 greater? 4 greater? n
greater?
Need Help, Thanks!

 

[stapel]

In terms of rational functions, what happens if the degree of the numerator is two greater than the degree of the denominator? 3 greater? 4 greater? n
greater?
Need Help, Thanks!

When the degree was 1 greater, the asymptote was the horizontal line which resulted from the long polynomial division (and from ignoring the fractional part). When the degree is 2 greater, the long polynomial division will give you a quadratic. The "asymptote" will also be a quadratic. (That is to say, the graph, away from the middle and any vertical asymptotes, will approximate the associated quadratic's graph.)

You can review an illustrated discussion here.