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Mathematics · Grade 11

Functions, Domain and Algebraic Structure

Algebra II opens by sharpening the language of functions. Learners find domains and ranges in interval notation, including restrictions from denominators and square roots, analyze piecewise and absolute value functions, combine and compose functions (and find the domain of a composition), and use algebraic structure: testing whether functions are even or odd, decomposing composite functions, and computing average rates of change.

  • 4 lessons
  • About 125 minutes
  • Functions and structure check: 11 questions
  • Ways to answer: choose an answer, plot points, match pairs, type a number, put in order and sort into groups
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What learners will discover

  • Determine domain and range in interval notation, including restrictions from denominators, even roots and context.
  • Evaluate and analyze piecewise-defined and absolute value functions, including key points and zeros.
  • Add, subtract, multiply and compose functions, find the domain of a composition, and decompose a function into simpler parts.
  • Use algebraic structure to classify functions as even, odd or neither, and compute and interpret average rates of change.

Lessons

  1. Domain and range in interval notation 6 steps4 practiceabout 30 min
  2. Piecewise and absolute value functions 6 steps4 practiceabout 30 min
  3. Combining and composing functions 6 steps4 practiceabout 33 min
  4. Symmetry and rates of change 6 steps3 practiceabout 30 min
  5. Functions and structure check 11 questions at the end

Keep exploring

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Guide for grown-ups