Chapter 3: Polynomial and Rational Functions
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Course: MATH 141 (Precalculus I)
Overview
Polynomial and rational functions appear throughout calculus. Understanding their behavior—zeros, asymptotes, end behavior—is essential for curve sketching and limit calculations.
Source Material: OpenStax Precalculus Chapter 3 (CC BY 4.0)
Sections
| Section | Topic | Skills |
|---|---|---|
| 3.1 | Complex Numbers | Operations with complex numbers |
| 3.2 | Quadratic Functions | Vertex form, completing the square |
| 3.3 | Power Functions and Polynomial Functions | Degree, leading coefficient |
| 3.4 | Graphs of Polynomial Functions | End behavior, turning points |
| 3.5 | Dividing Polynomials | Long division, synthetic division |
| 3.6 | Zeros of Polynomial Functions | Rational root theorem, factoring |
| 3.7 | Rational Functions | Vertical/horizontal asymptotes |
| 3.8 | Inverses and Radical Functions | Inverse of polynomial functions |
| 3.9 | Modeling Using Variation | Direct, inverse, joint variation |
Skills in This Chapter
What This Unlocks
Mastering these functions prepares you for:
- Chapter 4: Exponential functions (another function type)
- Stewart 1.2: Catalog of essential functions
- Stewart 2.3: Calculating limits (polynomial evaluation)
- Stewart 4.3: Curve sketching (combining all analysis)
| Previous | Up | Next |
|---|---|---|
| Chapter 2 | Precalculus | Chapter 4 |