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Mathematics · Grade 11

Rational Expressions and Functions

Learners treat rational expressions like fractions with variables: they simplify, multiply, divide, add and subtract them while tracking domain restrictions, solve rational equations and detect extraneous solutions, analyze rational functions (vertical and horizontal asymptotes, holes, transformations of 1/x), and model inverse variation, combined work rates and average cost.

  • 4 lessons
  • About 130 minutes
  • Rational expressions and functions check: 11 questions
  • Ways to answer: choose an answer, plot points, match pairs, type a number, sort into groups and true or false
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What learners will discover

  • Simplify, multiply, divide, add and subtract rational expressions, stating the restrictions on the variable.
  • Solve rational equations, check for and explain extraneous solutions.
  • Identify vertical and horizontal asymptotes, holes and intercepts of rational functions, including transformations of y = 1/x.
  • Model situations with rational functions: inverse variation, combined work rates and average cost.

Lessons

  1. Operations with rational expressions 6 steps4 practiceabout 32 min
  2. Rational equations and extraneous solutions 6 steps3 practiceabout 32 min
  3. Graphs of rational functions 6 steps4 practiceabout 33 min
  4. Rational models 6 steps4 practiceabout 28 min
  5. Rational expressions and functions check 11 questions at the end

Keep exploring

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Guide for grown-ups