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2.4 Rational Equations and Functions

Solving rational equations, analyzing asymptotes, discontinuities, and behavior of rational functions.

本节包含的知识点

  • 2.4.1 Solving Rational Equations — Methods for solving equations containing rational expressions, including clearing denominators and checking for extraneous solutions.
  • 2.4.2 Vertical Asymptotes and Discontinuities — Identifying vertical asymptotes from denominators and distinguishing between removable discontinuities (holes) and non-removable discontinuities.
  • 2.4.3 Horizontal and Oblique Asymptotes — Determining horizontal asymptotes using degree comparison and finding oblique asymptotes through polynomial long division.
  • 2.4.4 Analyzing Rational Function Behavior — Studying domain, range, end behavior, and sign analysis of rational functions to sketch accurate graphs.
  • 2.4.5 Rational Inequalities — Solving inequalities involving rational expressions using sign analysis and number line methods.
  • 2.4.6 Applications of Rational Functions — Real-world applications including work problems, rate problems, and concentration problems modeled by rational functions.