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Mathematics · Grade 12

Polynomial and Rational Function Analysis

Learners analyze polynomial and rational functions as a precalculus student should: complete factorization over the complex numbers, end behavior and turning points, sign charts for polynomial inequalities, a full analysis of rational graphs including holes and slant asymptotes, and rational inequalities in context, such as keeping an average cost below a target.

  • 4 lessons
  • About 130 minutes
  • Polynomial and rational analysis check: 11 questions
  • Ways to answer: choose an answer, plot points, match pairs, type a number, place on a number line and sort into groups
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What learners will discover

  • Analyze polynomial functions: end behavior, real and complex zeros with multiplicity, factorization over the complex numbers and turning points.
  • Solve polynomial inequalities with sign charts and express solutions in interval notation.
  • Analyze rational functions completely: holes, vertical, horizontal and slant asymptotes, and intercepts.
  • Solve rational inequalities and interpret their solutions in context.

Lessons

  1. Polynomials over the complex numbers 6 steps3 practiceabout 30 min
  2. Polynomial inequalities and sign charts 5 steps3 practiceabout 32 min
  3. Full analysis of rational functions 6 steps4 practiceabout 34 min
  4. Rational inequalities 6 steps3 practiceabout 30 min
  5. Polynomial and rational analysis check 11 questions at the end

Keep exploring

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Guide for grown-ups