In this activity, the students use piecewise functions to describe and model everyday situations.
Before the Activity
The students should have covered the topics concerning linear functions and piecewise functions. They should be able to find the tabular and graphical representations of a function given its symbolic representation. They should also be able to find the symbolic representation of a function given its graphical representation.
The instructor should install the piecewise_functions.tns in every TI-Nspire. The students should be divided into pairs, and each one must have a copy of piecewise_functions_student handout.
During the Activity
This activity consists of two problems. In the first problem, a series of graphs are given to the student. The student should come up with stories of everyday situations that can be modeled using the given graphs.
The student is then asked to give the units of measurement and scale of the graphs that would best fit the stories they came up with. The students are also asked to give the range and domain of the graphs.
In the second problem, an everyday situation is described, and the students have to choose the graph that best models it. The students should then write a table of values for the chosen graph.
Finally, the students are asked to give the algebraic representation of the graph. Piecewise functions are used in both parts. After the students have completed the assignment, the instructor should lead a group discussion in which the concepts learned are reviewed.
After the Activity
The students should model other everyday situations using piecewise functions.