Chapter 3: Polynomial and Rational Functions
God made the integers; all else is the work of man.
— Leopold Kronecker
Why This Matters
Polynomials are the building blocks of algebra. They’re simple enough to analyze completely, yet powerful enough to approximate almost any function.
Rational functions — ratios of polynomials — reveal the behavior of systems at their limits: what happens as \(x \to \infty\)? As \(x \to 0\)?
Sections
| Section | Topic | Key Skill | Status |
|---|---|---|---|
Quadratic Functions |
Vertex form, optimization |
[ ] Not Started |
|
Polynomial Functions |
Degree, end behavior |
[ ] Not Started |
|
Division of Polynomials |
Long division, synthetic |
[ ] Not Started |
|
Zeros of Polynomials |
Factor theorem, multiplicity |
[ ] Not Started |
|
Rational Functions |
Asymptotes, holes |
[ ] Not Started |
|
Polynomial and Rational Inequalities |
Sign analysis |
[ ] Not Started |
|
Variation |
Direct, inverse, joint |
[ ] Not Started |