College Algebra and Trigonometry: Building Concepts and Connections Book

Chapters 1-11 conclude with a Chapter Summary and Review Exercises. P. Algebra and Geometry Review P.1 The Real Number System P.2 Integer Exponents and Scientific Notation P.3 Roots, Radicals, and Rational Exponents P.4 Polynomials P.5 Factoring P.6 Rational Expressions P.7 Geometry Formulas P.8 Solving Basic Equations 1. Functions, Graphs, and Applications 1.1 Functions 1.2 Graphs of Functions 1.3 Linear Functions 1.4 Modeling with Linear Functions; Variation 1.5 Intersections of Lines and Linear Inequalities 2. More About Functions and Coordinate Geometry 2.1 Coordinate Geometry: Distance, Midpoints, and Circles 2.2 The Algebra of Functions 2.3 Transformations of the Graph of Functions 2.4 Symmetry and Other Properties of Functions 2.5 Equations and Inequalities Involving Absolute Value 2.6 Piecewise-Defined Functions 3. Quadratic Functions 3.1 Graphs of Quadratic Functions 3.2 Quadratic Equations 3.3 Complex Numbers and Quadratic Equations 3.4 Quadratic Inequalities 3.5 Equations Reducible to Quadratic Form; Rational and Radical Equations 4. Polynomial and Other Functions 4.1 Graphs of Polynomial Functions 4.2 More on Graphs of Polynomial Functions and Models 4.3 Division of Polynomials; The Remainder and Factor Theorems 4.4 Real Zeros of Polynomials; Solutions of Equations 4.5 The Fundamental Theorem of Algebra; Complex Zeros 4.6 Rational Functions 4.7 Polynomial and Rational Inequalities 5. Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions 5.3 Logarithmic Functions 5.4 Properties of Logarithms 5.5 Exponential and Logarithmic Equations 5.6 Exponential, Logistic, and Logarithmic Models 6. Trigonometric Functions 6.1 Angles and Their Measures 6.2 Trigonometric Functions Using the Right Triangle 6.3 Trigonometric Functions of Any Angle: Unit Circle Definition 6.4 Graphs of the Sine and Cosine Functions 6.5 Graphs of the Other Trigonometric Functions 6.6 Inverse Trigonometric Functions 7. Trigonometric Identities and Equations 7.1 Verifying Identities 7.2 Sum and Difference Identities 7.3 Multiple Angle Identities; Sum and Product Identities 7.4 Trigonometric Equations 8. Additional Topics in Trigonometry 8.1 The Law of Sines 8.2 The Law of Cosines 8.3 Vectors 8.4 Trigonometric Form of a Complex Number 9. Analytic Geometry 9.1 The Parabola 9.2 The Ellipse 9.3 The Hyperbola 9.4 General Form of Conic Sections; Rotation 9.5 Polar Coordinates and Graphs 9.6 Polar Equations of Conic Sections 9.7 Parametric Equations 10. Systems of Equations and Linear Inequalities 10.1 Systems of Linear Equations and Inequalities in Two Variables 10.2 Systems of Linear Equations in Three Variables 10.3 Solving Systems of Equations with Matrices 10.4 Operations with Matrices 10.5 Matrices and Inverses 10.6 Determinants and Cramer's Rule 10.7 Partial Fractions 10.8 Systems of Nonlinear Equations 11. More Topics in Algebra 11.1 Sequences 11.2 Sums of Terms of Sequences 11.3 General Sequences and Series 11.4 Counting Methods 11.5 Probability 11.6 The Binomial Theorem 11.7 Mathematical Induction Appendix. A TI-84 Keystroke Guide A.1 Keys on Your Calculator A.2 Getting Started A.3 Editing Your Work A.4 Entering Common Expressions A.5 Evaluating Functions A.6 Building Tables A.7 Graphing Linear, Quadratic, and Piecewise-Defined Functions A.8 Solving Equations A.9 Finding Maximum and Minimum of a Function A.10 Graphing Polynomial and Rational Functions and Inequalities A.11 Complex Numbers A.12 Fitting Curves to Data A.13 Matrices A.14 Sequences and Series