- Analyzing Functions
- Relations and Functions
- Domain and Range
- Intervals and Interval Notation
- Symmetry
- Zeroes and Intercepts
- Average Rate of Change
- Minimums and Maximums
- Discrete and Continuous Functions
- Increasing and Decreasing Functions
- Limits
- Limits and Asymptotes
- Infinite and Non-Existent Limits
- Function Families
- Linear and Absolute Value Function Families
- Square and Cube Function Families
- Square and Cube Root Function Families
- Graphing Cube Root Functions
- Transformations
- Vertical and Horizontal Transformations
- Stretching and Reflecting Transformations
- Combining Transformations
- Notation for Transformations
- Operations on Functions
- Composition of Functions
- Models of Functions
- Linear and Quadratic Models
- Cubic Models

- Polynomial and Rational Functions
- Quadratic Functions
- Methods for Solving Quadratic Functions
- Graphs of Quadratic Functions
- Graphing Polynomials
- Graphs of Polynomials Using Transformations
- Graphs of Polynomials Using Zeros
- Graphing Calculator to Analyze Polynomial Functions
- Rational Functions
- Analysis of Graphs of Rational Functions
- Graphs of Basic Rational Functions
- Graphs of Rational Functions when the Degrees are Equal
- Graphs of Rational Functions when the Degrees are not Equal
- Sign Test for Rational Function Graphs
- Analysis of Rational Functions
- Holes in Rational Functions
- Zeroes of Rational Functions
- Vertical Asymptotes
- Horizontal Asymptotes
- Oblique Asymptotes of Rational Functions
- Solving Rational Equations
- Forms of Inequalities
- Quadratic Inequalities
- Polynomial and Rational Inequalities
- Finding Zeros of Polynomials
- Long Division of Polynomials
- Synthetic Division of Polynomials
- Real Zeros of Polynomials
- Intermediate Value Theorem
- Fundamental Theorem of Algebra

- Exponential and Logarithmic Functions
- Functions and Inverses
- One-to-One Functions and Their Inverses
- Basic Exponential Functions
- Solving Exponential Equations
- Logarithmic Functions
- Graphs of Logarithmic Functions
- Properties of Logarithms
- Product and Quotient Properties of Logarithms
- Power Property of Logarithms
- Inverse Properties of Logarithms
- Common and Natural Logarithms
- Solving Logarithmic Equations
- Change of Base
- Exponential and Logarithmic Models
- Exponential Models
- Logarithmic Models
- Simple and Compound Interest
- The Number e
- Logistic Functions

- Polar Equations and Complex Numbers
- Polar Equations
- Polar Coordinates
- Polar and Cartesian Transformation
- Systems of Polar Equations
- Polar Equations of Conics
- Imaginary Numbers and Complex Numbers
- Imaginary Numbers
- Complex Numbers
- Quadratic Formula and Complex Sums
- Products and Quotients of Complex Numbers
- Polar Form of Complex Numbers
- Product and Quotient Theorems
- Powers and Roots of Complex Numbers

- Vector Analysis
- Two-Dimensional Vectors
- Positions and Midpoints in Two Dimensions
- Three-Dimensional Positions
- Vector Calculations
- Dot Products
- Scalar Projections
- Cross Products
- Vector Projection
- Planes in Space
- Distance Between a Point and a Plane
- Vector Direction
- Vector Equation of a Line
- Vector Analysis Applications

- Conic Sections
- Ellipses
- Ellipses Centered at the Origin
- Equation of an Ellipse
- Ellipses Not Centered at the Origin
- Focal Property of Ellipses
- Parabolas
- Parabolas with Vertex at the Origin
- Parabolas and the Distance Formula
- Parabolas with any Vertex
- Parabolas and Analytic Geometry
- Applications of Parabolas
- Hyperbolas
- Graphs of Hyperbolas Centered at the Origin
- Equations of Hyperbolas Centered at the Origins
- Hyperbolas with any Center
- Hyperbola Equations and the Focal Property
- Hyperbolas and Asymptotes
- Conic Sections and Dandelin Spheres
- General Forms of Conic Sections
- Classifying Conic Sections
- Equations of Circles
- Circles Centered at the Origin
- Circles Not Centered at the Origin
- Degenerate Conics
- Applications of Conics
- Solving Systems of Lines, Quadratics, and Conics

- Sequences, Series, and Mathematical Induction
- Formulas and Notation for Sequences and Series
- Recursive Formulas
- Explicit Formulas
- Sum Notation and Properties of Sigma
- Series Sums
- Partial Sums
- Series Sums and Gauss' Formula
- Problem Solving with Series Sums
- Mathematical Induction
- Inductive Proofs
- Induction and Factors
- Induction and Inequalities
- Sums of Geometric Series
- Sums of Finite Geometric Series
- Sums of Infinite Geometric Series
- Factorials and Combinations
- Binomial Theorem and Expansions
- Sequences
- Arithmetic Sequences
- Finding the nth Term Given the Common Difference and a Term
- Finding the nth Term Given Two Terms for an Arithmetic Sequence
- Geometric Sequences
- Finding the nth Term Given the Common Ratio and the First Term
- Finding the nth Term Given Two Terms for a Geometric Sequence
- Sums of Arithmetic Series
- Sums of Finite Arithmetic Series

- Introduction to Calculus
- Limits in Calculus
- Definition of a Limit
- One-Sided Limits
- Infinite Limits
- Polynomial Function Limits
- Rational Function Limits
- Applications of One-Sided Limits
- Tables to Find Limits
- Tangents to a Curve
- Instantaneous Rates of Change
- Derivatives
- Constant Derivatives and the Power Rule
- Derivatives of Sums and Differences
- Quotient Rule and Higher Derivatives
- Integrals
- Area Under the Curve
- Anti-Derivative
- Fundamental Theorem of Calculus

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