Use the vertical slider to select a family of rational functions to explore. Use the horizontal sliders to vary the coefficients in the function. Look particularly at the relationship between the equation and the points at which the graph cuts the axes, and any asymptotes (vertical, horizontal or oblique). Try to predict the shapes of the graphs.
What happens if you have the same factor in the numerator and denominator of the function? What happens if you have a repeated factor in the denominator of the function?