Polynomial and Rational Functions

Understanding polynomial and rational functions, their graphs, and behavior

This section contains 11 topics with 0 subtopics, 36 practice problems and 61 flashcards. Each topic includes comprehensive written notes, worked examples with detailed solutions, and interactive lessons for hands-on practice.

Topics Covered

• Polynomial Functions and End Behavior — Analyze polynomial functions, their zeros, multiplicity, and end behavior.
• Rational Functions and Asymptotes — Analyze rational functions including vertical, horizontal, and slant asymptotes.
• Polynomial Functions and End Behavior — Understanding polynomial functions, their graphs, and how to determine end behavior
• Transformations of Functions — Apply transformations including shifts, reflections, stretches, and compositions.
• Rational Functions and Asymptotes — Understanding rational functions, vertical asymptotes, horizontal asymptotes, and holes
• Polynomial Division and Remainder Theorem — Understanding polynomial long division, synthetic division, and the Remainder and Factor Theorems
• Partial Fraction Decomposition — Breaking down rational expressions into simpler fractions for integration and analysis
• Complex Numbers and Operations — Understand complex numbers, perform operations with complex numbers, and solve equations involving complex solutions.
• Fundamental Theorem of Algebra and Factoring — Apply the Fundamental Theorem of Algebra to find all roots of polynomials and completely factor polynomial expressions.
• Polynomial Inequalities — Solve polynomial inequalities using sign analysis, test points, and graphical methods.
• Rational Inequalities — Solve rational inequalities by finding critical values from zeros and vertical asymptotes, then using sign analysis.

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