Rational functions supply important examples and occur naturally in many contexts.
All polynomials are rational functions.
A polynomial is a rational functions with denominator 1. It is often better to use algebra and differential calculus to make a sketch which illustrates the important features, rather than using technology. The graphs of rational functions can be very complicated sporting bumps, holes, and asymptotes. Most graphing calculators do a lousy job of graphing rational functions unless you know how to tell them to do a good job. This involves adjusting window parameters and graphing the function in pieces which display all the important features and avoid numerical difficulties.