Rational Functions of Small Degree
Graphing rational functions is an important topic in precalculus and calculus classes. This Demonstration illustrates the important features of the graphs of these functions, showing both vertical and horizontal asymptotes, as well as the behavior at infinity. It is limited to two roots and two vertical asymptotes, but each is allowed to be repeated. This Demonstration can be used to illustrate the difference between the behavior of a graph near single roots and double roots.
Snapshot 1: a slant asymptote
Snapshot 2: both a horizontal asymptote and where a factor in the numerator cancels a factor in the denominator
Snapshot 3: the degree of the numerator is two more than the denominator; you can highlight the endpoint behavior by increasing the domain until the red and blue graphs become superimposed, or highlight the differences for small by reducing the size of the domain