In this lesson, students study functions and their graphs in context. They determine if the function is continuous or discrete based on context. They also produce graphs of functions, paying close attention to the appropriate domain and range, which are both restricted by the context. Note that the terms continuous and discrete will not be assessed, so these terms can be introduced if it is helpful, but it is not necessary to do so.
In the first activity, students decide whether plotted points in a graph representing a function should be connected or not, and in the second activity, students describe limits on the domain and range of a function representing a context. Both of these considerations are an important part of modeling with mathematics (MP4). This lesson prepares students to extend their understandings of domain and range to exponential functions in the associated Algebra I lesson.
- Determine whether a graph that represents a situation should be continuous or discrete.
- Interpret functions to analyze their domains.
- Let’s describe the domain of a function based on the context it models.