Piecewise-Defined Functions
Lesson Objective: This lab is designed to help students gain a better understanding of piecewise-defined functions. It would be used in a later unit once students have progressed to more advanced topics involving functions. Specifically, it may be used to explore how graphs are constructed from piecewise-defined functions, and how to define functions given a piecewise graph. Students will also explore domain and range in this activity as they move sliders to adjust the graphs of the piecewise-defined functions. Closed and open circles are used to mark the end points of each function, which serve as an additional visual aid to reinforce the domain restrictions on each function.
Lab Overview: This GeoGebra lab features several rational functions whose domains are defined by sliders. As students move each slider, constants and coefficients in the functions are changed, and thus the graphs of each function move to satisfy the new parameters. Closed and open circles are used to mark the end points of each function; this serves as an additional visual aid to reinforce the domain restrictions on each function.