Precalculus Study Library.

Rates of Change of Functions (average vs. instantaneous; secant/tangent slopes) · Rates of Change in Linear and Quadratic Functions · Polynomial Functions and Rates of Change · Polynomial Functions and Complex Zeros (Fundamental Theorem; real vs. complex roots) · Polynomial Functions and End Behavior (leading term; even/odd degree) · Polynomial Functions and Local/Global Behavior (local extrema; intervals of increase/decrease) · Rational Functions and Zeros (factoring; removable discontinuities) · Rational Functions and Vertical Asymptotes · Rational Functions and Horizontal Asymptotes (degree comparison) · Rational Functions and Oblique Asymptotes (polynomial long division) · Equivalent Representations of Polynomial and Rational Expressions · Transformations of Functions (translations, reflections, dilations) · Function Model Selection and Assumption Articulation · Function Model Construction and Application

Arithmetic Sequences (common difference; connection to linear functions) · Geometric Sequences (common ratio; connection to exponential functions) · Exponential Functions (base, growth/decay rates; domains/ranges) · Exponential Function Manipulation (properties of exponents; equivalent forms) · Exponential Function Context and Data Modeling · Competing Function Model Validation (residual plots) · Composition of Functions (f∘g; domain restrictions) · Inverse Functions (one-to-one functions; algebraic and graphical inverses) · Logarithmic Expressions (log definition; change of base) · Logarithmic Functions (domain, range, asymptotes; graph behavior) · The Number e and the Natural Logarithm · Logarithmic Function Manipulation (product, quotient, power rules) · Exponential and Logarithmic Equations and Inequalities · Exponential and Logarithmic Function Context and Data Modeling · Semi-Log Plots (linearizing exponential data; interpreting log-scale graphs)

Periodic Phenomena (period, midline, amplitude; identifying cycles) · Sine, Cosine, and Tangent (unit circle definitions; exact values at key angles) · Sine and Cosine Function Values (reference angles; all-quadrant evaluation) · Sine and Cosine Function Graphs (key features; transformations) · Sinusoidal Functions (A·sin(B(x–C))+D form; fitting to data) · Sinusoidal Function Transformations · Sinusoidal Function Context and Data Modeling · The Tangent Function (undefined values; period π; behavior near asymptotes) · Inverse Trigonometric Functions (restricted domains; range of arcsin/arccos/arctan) · Trigonometric Equations and Inequalities (general solutions; unit circle) · The Secant, Cosecant, and Cotangent Functions (reciprocal identities) · Equivalent Representations of Trigonometric Functions (Pythagorean identities) · Trigonometry and Polar Coordinates (r, θ; converting between polar and Cartesian) · Polar Function Graphs (circles, limaçons, rose curves; key features) · Rates of Change in Polar Functions

Parametric Functions (parametric equations; tracing curves; eliminating the parameter) · Implicitly Defined Functions and Conic Sections (circles, ellipses, parabolas, hyperbolas) · Vectors in Two Dimensions (magnitude, direction, component form) · Vectors in Three Dimensions (3D component form; distance) · Vector Operations (addition, scalar multiplication, linear combinations) · The Dot Product of Two Vectors (formula; geometric interpretation; angle between vectors) · Matrix Operations (addition, subtraction, scalar multiplication) · Matrix Multiplication · Matrices as Functions (linear transformations; mapping vectors) · Matrices Modeling Contexts · Inverses and Determinants (2×2 inverse; determinant; solving matrix equations) · Linear Systems and Matrices (augmented matrices; row reduction) · Vectors in Motion (velocity vectors; parametric motion models) · Matrix Composition and Transformations (composing transformations)