This applet will explore the relationship of a rational function h(x) = f(x)/g(x) and its quotient and remainder.

Enter the numerator, f(x) and the denominator, g(x) of a rational function into the algebra window.
Use the CAS window to find the quotient of two polynomials that make up a rational function.
Enter the quotient, q(x), and the remainder, r(x) in the Algebra window.
What happens to r(x) as x gets large? Why does this happen?
How do you see this in the graph of h(x) with its quotient, q(x)?