Asymptotes of Rational Functions

In using this applet, we will be able to investigate vertical and horizontal asymptotes of a rational function of the form f(x) = Ax^n/Bx^m + C (quotient of two polynomials). The function f(x) would have vertical asymptotes at the zeros of the denominator (set Bx^m + C =0 and solve for x). The horizontal asymptotes depend on the parameters A, B, C, and specially on n, and m. To begin, read the questions at the bottom of the graph, and click on the sliders to change the values of each parameter. Observe the changes and try to answer the questions

1. If you set n<m, what is a horizontal asymptote of f(x)?
2. what is n>m? Can you find any asymptotes?
3. Set n = m. Can you tell by changing the values of A and B, what a horizontal asymptote in the graph of f would be?
4. By changing the value of C, make a guess on what the vertical asymptotes would be and then solve it algebraically and compare answers?

Rocio Franklin, Created with GeoGebra