Characteristics of Functions

The Common Core State Standards include three functions in Algebra 1.

• linear
• exponential
• quadratic

Linear and quadratic functions are exhausted. Exponential functions are introduced with respect to making comparisons between arithmetic and geometric sequences but not exhausted. Absolute value functions are optional for Algebra 1; however, the spin-off from linear functions is seamless. And absolute value functions are perfect for initial practice with function transformations.

Several linear function concepts are introduced in MATH-8, but these are the same standards that are pushed to Accelerated Algebra 1 in the CCSS Accelerated Pathway outlined in Appendix A. The Retro Race activity contains a problem set that can be integrated throughout a linear functions unit or used as a cumulative review at the conclusion of the unit. (This activity stems from CPM Sample Chapters and LTF Training.)

A portion of the problem set highlights one of the participants in the race. Based on the information provided, students are prompted to create a table of values to view the participant's distance as a function of time and subsequently graph the results.

Characteristics of Functions Record Sheet

Students use the context of the situation to understand key features of the function including intercepts and intervals where the function is increasing, decreasing, positive, or negative.

This investigation highlights Common Core State Standard HSF-IF.B.4 that is included in 7th and 8th Accelerated Algebra 1.