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📐 Unit 1A — Polynomial Functions
1.1
Change in Tandem
How two quantities change together; covariation and function relationships
1.2
Rates of Change
Average rate of change and interpreting rates in context
1.3
Rates of Change in Linear and Quadratic Functions
Constant vs. non-constant rates; connecting slope to linear functions
1.4
Polynomial Functions and Rates of Change
How degree affects rate of change; concavity and inflection
1.5
Polynomial Functions and Complex Zeros
Real and complex roots, the Fundamental Theorem of Algebra
1.6
Polynomial Functions and End Behavior
Leading term test; what happens as x → ±∞
📐 Unit 1B — Rational Functions & Modeling
1.7
Rational Functions and End Behavior
Horizontal asymptotes; comparing degrees of numerator and denominator
1.8
Rational Functions and Zeros
Finding x-intercepts of rational functions; sign analysis
1.9
Rational Functions and Vertical Asymptotes
Where the denominator = 0; behavior near vertical asymptotes
1.10
Rational Functions and Holes
Removable discontinuities; cancelling common factors
1.11
Equivalent Representations of Polynomial and Rational Expressions
Binomial theorem, polynomial long division, slant asymptotes
1.12
Transformations of Functions
Translations, reflections, dilations — vertical and horizontal shifts
1.13
Function Model Selection and Assumption Articulation
Choosing the right model type (linear, polynomial, rational) for a context
1.14
Function Model Construction and Application
Building function models from data, tables, and real-world scenarios