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Summary
With a visual, graphical approach that emphasizes connections among concepts, this text helps readers make the most of their study time. The authors show how different mathematical ideas are tied together through their zeros, solutions, and "x"-intercepts theme; side-by-side algebraic and graphical solutions; calculator screens; and examples and exercises. By continually reinforcing the connections among various mathematical concepts as well as different solution methods, the authors lead readers to the ultimate goal of mastery and success. Basic Concepts of Algebra. Graphs, Functions, and Models. Functions, Equations, and Inequalities. Polynomial and Rational Functions. Exponential and Logarithmic Functions. The Trigonometric Functions. Trigonometric Identities, Inverse Functions, and Equations. Applications of Trigonometry. Systems of Equations and Matrices. Analytic Geometry Topics. Sequences, Series, and Combinatorics. For all readers interested in algebra and trigonometry.
Table of Contents
Chapter R: Basic Concepts of Algebra R.1 The Real-Number SystemR.2 Integer Exponents, Scientific Notation, and Order of OperationsR.3 Addition, Subtraction, and Multiplication of PolynomialsR.4 FactoringR.5 Rational ExpressionsR.6 Radical Notation and Rational ExponentsR.7 The Basics of Equation SolvingChapter 1: Graphs, Functions, and Models 1.1 Introduction to Graphing1.2 Functions and Graphs1.3 Linear Functions, Slope, and Applications1.4 Equations of Lines and Modeling1.5 More on Functions1.6 The Algebra of Functions1.7 Symmetry and TransformationsChapter 2: Functions, Equations, and Inequalities2.1 Linear Equations, Functions, and Models2.2 The Complex Numbers2.3 Quadratic Equations, Functions, and Models2.4 Analyzing Graphs of Quadratic Functions2.5 More Equation Solving2.6 Solving Linear InequalitiesChapter 3: Polynomial and Rational Functions3.1 Polynomial Functions and Models3.2 Graphing Polynomial Functions3.3 Polynomial Division; The Remainder and Factor Theorems3.4 Theorems about Zeros of Polynomial Functions3.5 Rational Functions3.6 Polynomial and Rational Inequalities3.7 Variation and ApplicationsChapter 4: Exponential and Logarithmic Functions 4.1 Inverse Functions4.2 Exponential Functions and Graphs4.3 Logarithmic Functions and Graphs4.4 Properties of Logarithmic Functions4.5 Solving Exponential and Logarithmic Equations4.6 Applications and Models: Growth and Decay; Compound InterestChapter 5: The Trigonometric Functions 5.1 Trigonometric Function of Acute Angles5.2 Applications of Right Triangles5.3 Trigonometric Functions of Any Angle5.4 Radians, Arc Length, and Angular Speed5.5 Circular Functions: Graphs and Properties5.6 Graphs of Transformed Sine and Cosine FunctionsChapter 6: Trigonometric Identities, Inverse Functions, and Equations 6.1 Identities: Pythagorean and Sum and Difference6.2 Identities: Cofunction, Double-Angle, and Half-Angle6.3 Proving Trigonometric Identities6.4 Inverses of the Trigonometric Functions6.5 Solving Trigonometric EquationsChapter 7: Applications of Trigonometry 7.1 The Law of Sines7.2 The Law of Cosines7.3 Complex Numbers: Trigonometric Form7.4 Polar Coordinates and Graphs7.5 Vectors and Applications7.6 Vector OperationsChapter 8: Systems of Equations and Matrices8.1 Systems of Equations in Two Variables8.2 Systems of Equations in Three Variables8.3 Matrices and Systems of Equations8.4 Matrix Operations8.5 Inverses of Matrices8.6 Determinants and Cramer's Rule8.7 Systems of Inequalities and Linear Programming8.8 Partial FractionsChapter 9: Analytic Geometry Topics 9.1 The Parabola9.2 The Circle and the Ellipse9.3 The Hyperbola9.4 Nonlinear Systems of Equations and Inequalities9.5 Rotation of Axes9.6 Polar Equations of Conics9.7 Parametric EquationsChapter 10: Sequences, Series, and Combinatorics 10.1 Sequences and Series10.2 Arithmetic Sequences and Series10.3 Geometric Sequences and Series10.4 Mathematical Induction10.5 Combinatorics: Permutations10.6 Combinatorics: Combinations10.7 The Binomial Theorem10.8 Probability Appendix Basic Concepts of Geometry