Defining rational functions

To bring this back to our original purpose, let's restate our definition of a rational function. A rational function is a function that can be expressed in the form , where is a polynomial and is a non-zero polynomial. A polynomial function is a function of the form where each of the s are real numbers and is a non-negative integer.

Enter an example of a rational function below.

Which of the following functions are polynomials?

Check all that apply

Which of the following functions are rational?

Check all that apply

State a general relationship between polynomial functions and rational functions. (Hint: think squares and rectangles.)

A key distinction between polynomial and rational functions is that, while all polynomials are continuous, not all rational functions are continuous. Plot a rational function below that has a discontinuity at .

If is a rational function with a discontinuity at , what can you conclude?

Plot an example of a rational function that (a) is not a polynomial and also (b) has no discontinuities.