Chapter 3 Polynomial and Rational Functions

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Polynomial and rational functions can model quantities that grow, turn, cross important thresholds, or approach limiting values. In this chapter, you will connect polynomial equations with their graphs by studying end behaviour, zeros, multiplicity, intercepts, and turning points. Polynomial division, the Remainder Theorem, and the Rational Zeros Theorem will provide tools for finding and interpreting roots. Complex numbers and the Fundamental Theorem of Algebra will extend these ideas beyond the real number system. The chapter concludes with rational functions, where you will analyze domains, holes, intercepts, and vertical, horizontal, and slant asymptotes to build accurate graphs and meaningful models.