Introduction to Graphs and the Graphing Calculator.
R. Basic Concepts of Algebra.
The Real-Number System.
Integer Exponents, Scientific Notation, and Order of Operations.
Addition, Subtraction, and Multiplication of Polynomials.
Factoring.
Rational Expressions.
Radical Notation and Rational Exponents.
The Basics of Equation Solving.
1. Graphs, Functions, and Models.
Functions, Graphs, and Graphers.
Linear Functions, Slope, and Applications.
Modeling: Data Analysis, Curve Fitting, and Linear Regression.
More on Functions.
Symmetry and Transformations.
Variation and Applications.
Distance, Midpoints, and Circles.
2. Functions and Equations: Zeros and Solutions.
Zeros of Linear Functions and Models.
The Complex Numbers.
Zeros of Quadratic Functions and Models.
Analyzing Graphs of Quadratic Functions.
Modeling: Data Analysis, Curve Fitting, and Quadratic Regression.
Zeros and More Equation Solving.
Solving Inequalities.
3. Polynomial and Rational Functions.
Polynomial Functions and Models.
Polynomial Division; The Remainder and Factor Theorems.
Theorems about Zeros of Polynomial Functions.
Rational Functions.
Polynomial and Rational Inequalities.
4. Exponential and Logarithmic Functions.
Composite and Inverse Functions.
Exponential Functions.
Logarithmic Functions and Graphs.
Properties of Logarithmic Functions.
Solving Exponential and Logarithmic Equations.
Applications and Models: Growth and Decay.
5. The Trigonometric Functions.
Trigonometric Functions of Acute Angles.
Applications of Right Triangles.
Trigonometric Functions of Any Angle.
Radians, Arc Length, and Angular Speed.
Circular Functions: Graphs and Properties.
Graphs of Transformed Sine and Cosine Functions.
6. Trigonometric Identities, Inverse Functions, and Equations.
Identities: Pythagorean and Sum and Difference.
Identities: Cofunction, Double-Angle, and Half-Angle.
Proving Trigonometric Identities.
Inverses of the Trigonometric Functions.
Solving Trigonometric Equations.
7. Applications of Trigonometry.
The Law of Sines.
The Law of Cosines.
Complex Numbers: Trigonometric Form.
Polar Coordinates and Graphs.
Vectors and Applications.
Vector Operations.
8. Systems and Matrices.
Systems of Equations in Two Variables.
Systems of Equations in Three Variables.
Matrices and Systems of Equations.
Matrix Operations.
Inverses of Matrices.
Systems of Inequalities and Linear Programming.
Partial Fractions.
9. Conic Sections.
The Parabola.
The Circle and the Ellipse.
The Hyperbola.
Nonlinear Systems of Equations.
10. Sequences, Series, and Combinatorics.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
Mathematical Induction.
Combinatorics: Permutations.
Combinatorics: Combinations.
The Binomial Theorem.
Probability.
Appendixes.
A. Descartes' Rule of Signs.
B. Determinants and Cramer's Rule.
C. Parametric Equations.

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