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1.4 Polynomial Functions and Rates of Change

Part of Polynomial and Rational Functions in AP® Precalculus. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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In Unit 1.4 of AP Precalculus, you look at how the degree n of a polynomial function dictates its overall rate of change and long-term behavior. As the input variable x becomes extremely large (positive or negative), the term with the highest degree,
anxna_n x^n
dominates the function. The rate at which a polynomial grows or decays over large intervals is determined entirely by this leading term. For any polynomial function f(x), the average rate of change over an interval [a,b] is given by:
f(b)−f(a)b−a\frac{f(b) - f(a)}{b - a}

In this unit

14 lessons

  1. 1.1Change in TandemPreview lesson
  2. 1.2Rates of ChangePreview lesson
  3. 1.3Rates of Change in Linear and Quadratic FunctionsPreview lesson
  4. 1.4Polynomial Functions and Rates of ChangeThis lesson
  5. 1.5Polynomial Functions 2 and Complex ZerosPreview lesson
  6. 1.6Polynomial Functions and End BehaviorOpen lesson
  7. 1.7Rational Functions and End BehaviorOpen lesson
  8. 1.8Rational Functions and ZerosOpen lesson
  9. 1.9Rational Functions and Vertical AsymptotesOpen lesson
  10. 1.10Rational Functions and HolesOpen lesson
  11. 1.11Equivalent Representations of Polynomial and Rational ExpressionsOpen lesson
  12. 1.12Transformations of FunctionsOpen lesson
  13. 1.13Function Model Selection and Assumption ArticulationOpen lesson
  14. 1.14Function Model Construction and ApplicationOpen lesson

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