As you have discovered in this module, rational functions behave much differently than the linear and other polynomial functions you examined previously in your study of algebra. Rational functions have asymptotes, breaks in continuity, restricted domains, and varying end behavior patterns. Yet rational functions are tremendously helpful in exploring rates of change in the world around us. A rate of change is simply “quantity per quantity.” If quantity A is measured by x+7, and quantity B is measured by 3x-5, then, as the variable increases or decrease, the rate of change in quantity A per each quantity B is the rational function .

In another module, you will explore a family of functions which also is tremendously helpful in describing and evaluating rates of change: exponential functions. There, you will explore additional rate problems, such as the growth of an animal population, or the decay of radioactive material, over time.