<h1> Precalculus: Graphs & Models </h1><h3> Chapter 1: Functions and Graphs <h3><blockquote> <h4> 1.1, Rectangular Coordinates; Graphing Circles and Other Relations <h4> 1.2, Linear Equations and Rates of Change <h4> 1.3, Functions, Function Notation, and the Graph of a Function <h4> 1.4, Linear Functions, Special Forms, and More on Rates of Change <h4> 1.5, Solving Equations and Inequalities Graphically; Formulas and Problem Solving<h4> 1.6, Linear Function Models and Real Data</blockquote> <h3> Chapter 2: Relations, More on Functions<blockquote> <h4> 2.1, Analyzing the Graph of a Function<h4>2.2, The Toolbox Functions and Transformations <h4>2.3, Absolute Value Functions, Equations, and Inequalities<h4>2.4, Rational and Radical Functions; More on the Domain<h4>2.5, Piecewise-Defined Functions<h4>2.6, Variation: The Toolbox Functions in Action</blockquote><h3> Chapter 3: Quadratic Functions and Operations on Functions<blockquote> <h4> 3.1, Complex Numbers <h4> 3.2, Solving Quadratic Equations and Inequalities <h4> 3.3, Quadratic Functions and Applications <h4> 3.4, Quadratic Models; More on Rates of Change <h4> 3.5, The Algebra of Functions<h4> 3.6, Composition of Functions and the Difference Quotient</blockquote><h3> Chapter 4: Polynomial and Rational Functions<blockquote> <h4> 4.1, Synthetic Division; the Remainder and Factor Theorems<h4> 4.2, The Zeros of Polynomial Functions<h4> 4.3, Graphing Polynomial Functions<h4> 4.4, Graphing Rational Functions<h4> 4.5, Additional Insights into Rational Functions<h4> 4.6, Polynomial and Rational Inequalities</blockquote><h3> Chapter 5: Exponential and Logarithmic Functions<blockquote> <h4> 5.1, One-to-One and Inverse Functions<h4> 5.2, Exponential Functions<h4> 5.3, Logarithms and Logarithmic Functions<h4> 5.4, Properties of Logarithms<h4> 5.5, Solving Exponential and Logarithmic Equations<h4> 5.6, Applications from Business, Finance, and Science<h4> 5.7, Exponential, Logarithmic, and Logistic Equation Models</blockquote><h3> Chapter 6: Introduction to Trigonometry<blockquote> <h4> 6.1, Angle Measure, Special Triangles, and Special Angles<h4> 6.2, Unit Circles and the Trigonometry of Real Numbers<h4> 6.3, Graphs of Sine and Cosine Functions<h4> 6.4, Graphs of the Cosecant, Secant, Tangent, and Cotangent Functions<h4> 6.5, Transformations and Applications of Trigonometric Graphs<h4> 6.6, The Trigonometry of Right Triangles<h4> 6.7, Trigonometry and the Coordinate Plane<h4> 6.8, Trigonometric Equation Models</blockquote><h3> Chapter 7: Trigonometric Identities, Inverses, and Equations<blockquote> <h4> 7.1, Fundamental Identities and Families of Identities<h4> 7.2, More on Verifying Identities <h4> 7.3, The Sum and Difference Identities<h4> 7.4, The Double-Angle, Half-Angle and Product-to-Sum Identities<h4> 7.5, The Inverse Trigonometric Functions and their Applications<h4> 7.6, Solving Basic Trig Equations<h4> 7.7, General Trig Equations and Applications</blockquote><h3> Chapter 8: Applications of Trigonometry<blockquote> <h4> 8.1, Oblique Triangles and the Law of Sines<h4> 8.2, The Law of Cosines; the Area of a Triangle<h4> 8.3, Vectors and Vector Diagrams<h4> 8.4, Vector Applications and the Dot Product<h4> 8.5, Complex Numbers in Trigonometric Form<h4> 8.6, De Moivre’s Theorem and the Theorem on nth Roots</blockquote><h3> Chapter 9: Systems of Equations ad Inequalities; Matrices<blockquote> <h4> 9.1, Linear Systems in Two Variables with Applications<h4> 9.2, Linear Systems in Three Variables with Applications <h4> 9.3, Systems of Inequalities and Linear Programming<h4> 9.4, Partial Fraction Decomposition<h4> 9.5, Solving Linear Systems Using Matrices and Row Operations<h4> 9.6, The Algebra of Matrices<h4> 9.7, Solving Linear Systems Using Matrix Equations<h4> 9.8, Applications of Matrices and Determinants: Cramer’s Rule, Geometry, and More</blockquote><h3> Chapter 10: Analytical Geometry and the Conic Sections<blockquote> <h4> 10.1, A Brief Introduction to Analytic Geometry<h4> 10.2, The Circle and the Ellipse <h4> 10.3, The Hyperbola<h4> 10.4, The Analytic Parabola<h4> 10.5, Nonlinear Systems of Equations and Inequalities<h4> 10.6, Polar Coordinates, Equations, and Graphs<h4> 10.7, More on the Conic Sections: Rotation of Axes and Polar Form<h4> 10.8, Parametric Equations and Graphs</blockquote><h3> Chapter 11: Additional Topics in Algebra <blockquote> <h4> 11.1, Sequences and Series<h4> 11.2, Arithmetic Sequences<h4> 11.3, Geometric Sequences<h4> 11.4, Mathematical Induction<h4> 11.5, Counting Techniques<h4> 11.6, Introduction to Probability<h4> 11.7, The Binomial Theorem</blockquote><h3> Chapter 12: Bridges to Calculus – An Introduction to Limits<blockquote> <h4> 12.1, An Introduction to Limits Using Tables and Graphs <h4> 12.2, The Properties of Limits <h4> 12.3, Continuity and More on Limits <h4> 12.4, Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve</blockquote><h3> Appendix A: A Review of Basic Concepts and Skills<blockquote> <h4> A.1, Algebraic Expressions and the Properties of Real Numbers<h4> A.2, Exponents, Scientific Notation, and a Review of Polynomials<h4> A.3, Solving Linear Equations and Inequalities<h4> A.4, Factoring Polynomials and Solving Equations by Factoring<h4> A.5, Rational Expressions and Equations<h4> A.6, Radicals, Rational Exponents, and Radical Equations</blockquote><h3> Appendix B: Proof Positive - A Selection of Proofs from Precalculus<h3> Appendix C: More on Synthetic Division <h3> Appendix D: Reduced Row-Echelon Form and More on Matrices<h3> Appendix E: The Equation of a Conic<h3> Appendix F: Families of Polar Curves <h3> Online Appendices <blockquote> <h4> AO.1, The Language, Notation, and Numbers of Mathematics<h4> AO.2, Geometry Review with Unit Conversions</blockquote>
