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?
Which of the following functions are rational?
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?