Glossary for Lesson 23: Piecewise and Rational Functions
A piecewise function is a function that is made up of pieces of different functions in different parts of its domain. We could define a piecewise function like this:
Notice here that each part, or each so-called subfunction, of the piecewise function is paired with a certain part of the domain of . Graphs of piecewise functions sometimes end up looking really interesting. Here, for example, is the graph of the function shown above:
A step function is a piecewise function whose parts are constant functions, or horizontal lines. A step function might look something like this:
where the equation of the function is
A rational function is any function that is a ratio of two polynomials. That is, a rational function is of the form , where and are both polynomials and .
Here are some examples of rational functions:
All polynomial functions are technically rational functions, since any polynomial can be written as , and is a polynomial of order zero.