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Mathematics · Grade 12

Advanced Functions and Modeling Readiness

Precalculus opens with building functions from situations: writing explicit formulas from geometry and business contexts, describing processes recursively, composing and inverting functions to answer chained and reverse questions, and analyzing how a model behaves on intervals with average rates of change, extreme values and domain limits. Learners finish by choosing and defending a model family for a purpose.

  • 4 lessons
  • About 125 minutes
  • Advanced functions check: 10 questions
  • Ways to answer: choose an answer, match pairs, type a number, sort into groups, true or false and write a short answer
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What learners will discover

  • Build functions that describe relationships in context, as explicit expressions or recursive processes, including their sensible domains.
  • Compose and decompose functions to model chained processes, and use inverse functions to answer reverse questions.
  • Analyze a model's behavior on intervals using average rates of change, increasing and decreasing intervals and extreme values.
  • Choose an appropriate function family and parameters for a modeling purpose and justify the choice.

Lessons

  1. Building functions from situations 6 steps3 practiceabout 32 min
  2. Composing and inverting models 6 steps3 practiceabout 30 min
  3. Analyzing behavior on intervals 5 steps3 practiceabout 32 min
  4. Choosing a model family 5 steps2 practiceabout 28 min
  5. Advanced functions check 10 questions at the end

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