Teaching Algebra Chapter 7-Function Families

When examining a real situation that we want to model with mathematics, recognizing particular behaviors and knowing which function families they are consistent with can help determine which functions might be best to model that situation. In this chapter, teachers will examine multiple representations of function families including, geometric objects, DynaGraphs and Cartesian graphs. Teachers will explore function families through geometric transformations, and parameter explorations using sliders in dynamic mathematics software. Finally, teachers will consider the role of context in mathematical modeling tasks to build an understanding of the sine function family.

This chapter could be used alongside four Modules within the Examining Students’ Practices (ESP) in Algebra and Function:

Module 4: Characteristics of Function Families
Module 6: Key Features of Quadratic Functions
Module 7: Key Features of the Sine Functions
Module 8: Using Dynagraphs to Explore Functions