Precalculus: A Prelude to Calculus

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Cover Title Page Copyright About the Author Contents Preface to the Instructor Acknowledgments Preface to the Student Chapter 0 The Real Numbers 0.1 The Real Line Construction of the Real Line Is Every Real Number Rational? Problems 0.2 Algebra of the Real Numbers Commutativity and Associativity The Order of Algebraic Operations The Distributive Property Additive Inverses and Subtraction Multiplicative Inverses and the Algebra of Fractions Symbolic Calculators Exercises, Problems, and Worked-out Solutions 0.3 Inequalities, Intervals, and Absolute Value Positive and Negative Numbers Inequalities Intervals Absolute Value Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions Chapter 1 Functions and Their Graphs 1.1 Functions Definition and Examples The Domain of a Function The Range of a Function Functions via Tables Exercises, Problems, and Worked-out Solutions 1.2 The Coordinate Plane and Graphs The Coordinate Plane The Graph of a Function Determining the Domain and Range from a Graph Which Sets Are Graphs of Functions? Exercises, Problems, and Worked-out Solutions 1.3 Function Transformations and Graphs Vertical Transformations: Shifting, Stretching, and Flipping Horizontal Transformations: Shifting, Stretching, Flipping Combinations of Vertical Function Transformations Even Functions Odd Functions Exercises, Problems, and Worked-out Solutions 1.4 Composition of Functions Combining Two Functions Definition of Composition Decomposing Functions Composing More than Two Functions Function Transformations as Compositions Exercises, Problems, and Worked-out Solutions 1.5 Inverse Functions The Inverse Problem One-to-one Functions The Definition of an Inverse Function The Domain and Range of an Inverse Function The Composition of a Function and Its Inverse Comments About Notation Exercises, Problems, and Worked-out Solutions 1.6 A Graphical Approach to Inverse Functions The Graph of an Inverse Function Graphical Interpretation of One-to-One Increasing and Decreasing Functions Inverse Functions via Tables Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions Chapter 2 Linear, Quadratic, Polynomial, and Rational Functions 2.1 Lines and Linear Functions Slope The Equation of a Line Parallel Lines Perpendicular Lines Exercises, Problems, and Worked-out Solutions 2.2 Quadratic Functions and Conics Completing the Square and the Quadratic Formula Parabolas and Quadratic Functions Circles Ellipses Hyperbolas Exercises, Problems, and Worked-out Solutions 2.3 Exponents Positive Integer Exponents Defining x° Negative Integer Exponents Roots Rational Exponents Properties of Exponents Exercises, Problems, and Worked-out Solutions 2.4 Polynomials The Degree of a Polynomial The Algebra of Polynomials Zeros and Factorization of Polynomials The Behavior of a Polynomial Near ±∞ Graphs of Polynomials Exercises, Problems, and Worked-out Solutions 2.5 Rational Functions The Algebra of Rational Functions Division of Polynomials The Behavior of a Rational Function Near ±∞ Graphs of Rational Functions Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions Chapter 3 Exponential Functions, Logarithms, and e 3.1 Logarithms as Inverses of Exponential Functions Exponential Functions Logarithms Base 2 Logarithms with Any Base Common Logarithms and the Number of Digits Exercises, Problems, and Worked-out Solutions 3.2 The Power Rule for Logarithms Logarithm of a Power Radioactive Decay and Half-Life Change of Base Exercises, Problems, and Worked-out Solutions 3.3 The Product and Quotient Rules for Logarithms Logarithm of a Product Logarithm of a Quotient Earthquakes and the Richter Scale Sound Intensity and Decibels Star Brightness and Apparent Magnitude Exercises, Problems, and Worked-out Solutions 3.4 Exponential Growth Functions with Exponential Growth Population Growth Compound Interest Exercises, Problems, and Worked-out Solutions 3.5 e and the Natural Logarithm Estimating Area Using Rectangles Defining e Defining the Natural Logarithm Properties of the Exponential Function and Natural Logarithm Exercises, Problems, and Worked-out Solutions 3.6 Approximations and Area with e and ln Approximation of the Natural Logarithm Approximations with the Exponential Function An Area Formula Exercises, Problems, and Worked-out Solutions 3.7 Exponential Growth Revisited Continuously Compounded Interest Continuous Growth Rates Doubling Your Money Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions Chapter 4 Trigonometric Functions 4.1 The Unit Circle The Equation of the Unit Circle Angles in the Unit Circle Negative Angles Angles Greater than 360° Length of a Circular Arc Special Points on the Unit Circle Exercises, Problems, and Worked-out Solutions 4.2 Radians A Natural Unit of Measurement for Angles The Radius Corresponding to an Angle Length of a Circular Arc Area of a Slice Special Points on the Unit Circle Exercises, Problems, and Worked-out Solutions 4.3 Cosine and Sine Definition of Cosine and Sine The Signs of Cosine and Sine The Key Equation Connecting Cosine and Sine The Graphs of Cosine and Sine Exercises, Problems, and Worked-out Solutions 4.4 More Trigonometric Functions Definition of Tangent The Sign of Tangent Connections Among Cosine, Sine, and Tangent The Graph of Tangent Three More Trigonometric Functions Exercises, Problems, and Worked-out Solutions 4.5 Trigonometry in Right Triangles Trigonometric Functions via Right Triangles Two Sides of a Right Triangle One Side and One Angle of a Right Triangle Exercises, Problems, and Worked-out Solutions 4.6 Trigonometric Identities The Relationship Among Cosine, Sine, and Tangent Trigonometric Identities for the Negative of an Angle Trigonometric Identities with π/2 Trigonometric Identities Involving a Multiple of π Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions Chapter 5 Trigonometric Algebra and Geometry 5.1 Inverse Trigonometric Functions The Arccosine Function The Arcsine Function The Arctangent Function Exercises, Problems, and Worked-out Solutions 5.2 Inverse Trigonometric Identities Composition of Trigonometric Functions and Their Inverses More Inverse Functions More Compositions with Inverse Trigonometric Functions The Arccosine, Arcsine, and Arctangent of -t Arccosine Plus Arcsine Exercises, Problems, and Worked-out Solutions 5.3 Using Trigonometry to Compute Area The Area of a Triangle via Trigonometry Ambiguous Angles The Area of a Parallelogram via Trigonometry The Area of a Polygon Trigonometric Approximations Exercises, Problems, and Worked-out Solutions 5.4 The Law of Sines and the Law of Cosines The Law of Sines The Law of Cosines When to Use Which Law Exercises, Problems, and Worked-out Solutions 5.5 Double-Angle and Half-Angle Formulas The Cosine of 2θ The Sine of 2θ The Tangent of 2θ The Cosine and Sine of θ/2 The Tangent of θ/2 Exercises, Problems, and Worked-out Solutions 5.6 Addition and Subtraction Formulas The Cosine of a Sum and Difference The Sine of a Sum and Difference The Tangent of a Sum and Difference Products of Trigonometric Functions Exercises, Problems, and Worked-out Solutions 5.7 Transformations of Trigonometric Functions Amplitude Period Phase Shift Fitting Transformations of Trigonometric Functions to Data Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions Chapter 6 Sequences, Series, and Limits 6.1 Sequences Introduction to Sequences Arithmetic Sequences Geometric Sequences Recursively Defined Sequences Exercises, Problems, and Worked-out Solutions 6.2 Series Sums of Sequences Arithmetic Series Geometric Series Summation Notation Pascal’s Triangle The Binomial Theorem Exercises, Problems, and Worked-out Solutions 6.3 Limits Introduction to Limits Infinite Series Decimals as Infinite Series Special Infinite Series Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions Chapter 7 Polar Coordinates, Vectors, and Complex Numbers 7.1 Polar Coordinates Defining Polar Coordinates Converting from Polar to Rectangular Coordinates Converting from Rectangular to Polar Coordinates Graphs of Polar Equations Exercises, Problems, and Worked-out Solutions 7.2 Vectors An Algebraic and Geometric Introduction to Vectors Vector Addition Vector Subtraction Scalar Multiplication The Dot Product Exercises, Problems, and Worked-out Solutions 7.3 Complex Numbers The Complex Number System Arithmetic with Complex Numbers Complex Conjugates and Division of Complex Numbers Zeros and Factorization of Polynomials, Revisited Exercises, Problems, and Worked-out Solutions 7.4 The Complex Plane Complex Numbers as Points in the Plane Geometric Interpretation of Complex Multiplication and Division De Moivre’s Theorem Finding Complex Roots Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions Appendix: Area Circumference Squares, Rectangles, and Parallelograms Triangles and Trapezoids Stretching Circles and Ellipses Exercises, Problems, and Worked-out Solutions Photo Credits Index Colophon: Notes on Typesetting EULA