Polynomial and Rational Functions

Intermediate

Polynomial and rational functions are central to AP Precalculus. Polynomials are built from powers of x; their degree determines end behavior and the maximum number of zeros and turning points.

Rational functions arise when one polynomial is divided by another, introducing vertical asymptotes, horizontal asymptotes, and holes. Mastering zeros, multiplicity, end behavior, asymptotic analysis, and polynomial division prepares students for calculus concepts like limits and continuity.

Practice a little. See where you stand.

Part of:AP Precalculus -- Polynomial and Rational Functions AP Precalculus -- Polynomial and Rational Functions AP Precalculus -- Polynomial and Rational Functions

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Curriculum alignment— Standards-aligned

Grade level

Grades 9-12College+

Learning objectives

•Analyze polynomial functions using zeros, multiplicity, and end behavior to sketch graphs
•Identify vertical and horizontal asymptotes and holes in rational functions
•Apply the factor theorem and remainder theorem to factor and evaluate polynomials
•Perform polynomial long division and synthetic division