Understanding polynomial and rational functions, their graphs, and behavior
This section contains 11 topics with 0 subtopics, 36 practice problems and 60 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.
Click on any topic below to start studying. All materials are completely free.