Discontinuities of Rational Functions
Slide the sliders to see how varying the parameters a, b, c, and d affects the graph of the rational function. For better control, you may find it easiest to click one of the sliders and then use the arrow keys on your keyboard to adjust it. For some interesting visual effects, click on the checkbox to leave a "trace" of the graph.
What feature on the graph corresponds with the a value? The b value? c? d? The graph typically has three "branches." What causes one branch to collide with and then re-separate from its neighboring branch? Use the vocabulary of discontinuities to describe what you see. Is it possible to create more than two discontinuities for this function? If so, what is the maximum number of discontinuities? Is it possible to create less than two discontinuities for this function? If so, what is the minimum number of discontinuities?