This lesson picks up on the idea planted in the previous lesson about creating linear models for data. Specifically, in some situations where a quantity changes at different constant rates over different time intervals, we can model the situation with a piecewise linear function (MP4). Students look at temperature data, which changes at different, almost-constant rates during different parts of the day. They also use piecewise linear graphs to find information about the real-life situation they represent. The focus of this lesson is not necessarily to find equations for the piecewise linear functions (though students may choose to do so in some instances), but rather to study the graphs qualitatively and to compute and compare the different rates of change.
- Calculate the different rates of change of a piecewise linear function using a graph, and interpret (orally and in writing) the rates of change in context.
- Create a model of a non-linear function using a piecewise linear function, and describe (orally) the benefits of having more or less segments in the model.
Let’s explore functions built out of linear pieces.
- I can create graphs of non-linear functions with pieces of linear functions.