This lesson introduces a new type of function, a piecewise-defined function, that uses multiple descriptions to define the function on different parts of the domain. All piecewise functions in this lesson are presented in the context of situations where different rules apply for different input values, such as different bike rental prices for different rental durations and different postage rates for different letter weights.

In the bike rental activity, students are given the rules of a function and asked to graph the function. To do so, they pay attention to the boundary points, where one rule ends and another begins, and learn to use open and closed circles to indicate the correct output values for the input values that demarcate the rules.

Students are also introduced to the cases notation for piecewise functions. They practice interpreting it, which involves making use of the structure in the graph and in cases notation (MP7).