Investigating Functions

This Investigating Functions lesson plan also includes:

Late in algebra 2 or early in pre-calculus, learners are developing a kind of functional intuition. This worksheet goes a long way toward training this skill by helping to expose patterns of transformations through both general and specific examples. While effectively harnessing the graphing calculator to perform the tedious calculations and graphing, the class is expected to synthesize conclusions about function properties, and even apply this learning to newly created functions. A densely thought-provoking worksheet, no matter what the skill level of the participant.

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CCSS: Designed
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Instructional Ideas
  • Follow-up activities could include determining properties of functions modeling actual physical situations (perhaps from a physics class lab)
  • Ask learners to take properties and make a pairs game similar to Battleship or math pictionary
Classroom Considerations
  • Moderate level of graphing calculator competence is assumed; tips for transformations given for the TI-series of calculators, but no other
  • Color-coding different transformations might be intuitive to some, but be aware of colorblind students in the calssroom
  • Questions really make students work on understanding the properties of function classes
  • Careful balance of abstract rules and concrete examples of actual functions
  • Emphasis on both algebraic and graphical representation of functions, and links between the properties of both
  • Additional assessments available on the LTF website referenced on page iv is not readily found without school registration in the program