Precalculus: Graphs and Models
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The authors help students "see the math" through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on today's students and their needs, the authors lead students to mathematical understanding and, ultimately, success in class.
Chapter R Basic Concepts of AlgebraR.1 The Real-Number SystemR.2 Integer Exponents, Scientific Notation, and Order of OperationsR.3 Addition, Subtraction, and Multiplication of PolynomialsR.4 FactoringR.5 The Basics of Equation SolvingR.6 Rational ExpressionsR.7 Radical Notation and Rational ExponentsChapter 1 Graphs, Functions, and Models1.1 Introduction to Graphing1.2 Functions and Graphs1.3 Linear Functions, Slope, and Applications1.4 Equations of Lines and Modeling1.5 Linear Equations, Functions, Zeros, and Models1.6 Solving Linear InequalitiesChapter 2 More on Functions2.1 Increasing, Decreasing, and Piecewise Functions; Applications2.2 The Algebra of Functions2.3 The Composition of Functions2.4 Symmetry and Transformations2.5 Variation and ApplicationsChapter 3 Quadratic Functions and Equations; Inequalities3.1 The Complex Numbers3.2 Quadratic Equations, Functions, Zeros, and Models3.3 Analyzing Graphs of Quadratic Functions3.4 Solving Rational and Radical Equations3.5 Solving Absolute Value Equations and InequalitiesChapter 4 Polynomial And Rational Functions4.1 Polynomial Functions and Modeling4.2 Graphing Polynomial Functions4.3 Polynomial Division; The Remainder and Factor Theorems4.4 Theorems about Zeros of Polynomial Functions4.5 Rational Functions4.6 Polynomial and Rational InequalitiesChapter 5 Exponential and Logarithmic Functions5.1 Inverse Functions5.2 Exponential Functions and Graphs5.3 Logarithmic Functions and Graphs5.4 Properties of Logarithmic Functions5.5 Solving Exponential and Logarithmic Equations5.6 Applications and Models: Growth and Decay; Compound InterestChapter 6 The Trigonometric Functions6.1 Trigonometric Functions of Acute Angles6.2 Applications of Right Triangles6.3 Trigonometric Functions of Any Angle6.4 Radians, Arc Length, and Angular Speed6.5 Circular Functions: Graphs and Properties6.6 Graphs of Transformed Sine and Cosine FunctionsChapter 7 Trigonometric Identities, Inverse Functions, and Equations7.1 Identities: Pythagorean and Sum and Difference7.2 Identities: Cofunction, Double-Angle, and Half-Angle7.3 Proving Trigonometric Identities7.4 Inverses of the Trigonometric Functions7.5 Solving Trigonometric EquationsChapter 8 Applications of Trigonometry8.1 The Law of Sines8.2 The Law of Cosines8.3 Complex Numbers: Trigonometric Form8.4 Polar Coordinates and Graphs8.5 Vectors and Applications8.6 Vector OperationsChapter 9 Systems of Equations and Matrices9.1 Systems of Equations in Two Variables9.2 Systems of Equations in Three Variables9.3 Matrices and Systems of Equations9.4 Matrix Operations9.5 Inverses of Matrices9.6 Determinants and Cramer's Rule9.7 Systems of Inequalities and Linear Programming9.8 Partial FractionsChapter 10 Conic Sections10.1 The Parabola10.2 The Circle and the Eclipse10.3 The Hyperbola10.4 Nonlinear Systems of Equations and Inequalities10.5 Rotation of Axes10.6 Polar Equations of Conics10.7 Parametric EquationsChapter 11 Sequences, Series, and Combinatorics11.1 Sequences and Series11.2 Arithmetic Sequences and Series11.3 Geometric Sequences and Series11.4 Mathematical Induction11.5 Combinatorics: Permutations11.6 Combinatorics: Combinations11.7 The Binomial Theorem11.8 ProbabilityAppendixBasic Concepts from Geometry
