Contents. Unit 1 Algebraic, Exponential, and Logarithmic Functions. Chapter 1 Functions and Mathematical Models 1

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1 Contents Unit 1 Algebraic, Eponential, and Logarithmic Functions Chapter 1 Functions and Mathematical Models Functions: Graphicall, Algebraicall, Numericall, and Verball 3 Eploration: Paper Cup Analsis 1-2 Tpes of Functions Dilation and Translation of Function Graphs Eploration: Transformations from Graphs 1-4 Composition of Functions Eploration: Composition of Functions 1-5 Inverse Functions and Parametric Equations Eploration: Parametric Equations Graph 1-6 Reflections, Absolute Values, and Other Transformations Precalculus Journal Chapter Review and Test Chapter 2 Properties of Elementar Functions Shapes of Function Graphs Identifing Functions from Graphical Patterns Eploration: Graphical Patterns in Functions 2-3 Identifing Functions from Numerical Patterns Eploration: Patterns for Quadratic Functions 2-4 Properties of Logarithms Eploration: Introduction to Logarithms 2-5 Logarithms: Equations and Other Bases Logarithmic Functions Logistic Functions for Restrained Growth Eploration: The Logistic Function for Population Growth 2-8 Chapter Review and Test S T u D E N T E D I T I O N Chapter 3 Fitting Functions to Data Introduction to Regression for Linear Data Deviations, Residuals, and the Correlation Coefficient Regression for Nonlinear Data Linearizing Data and Logarithmic Graph Paper Eploration: Log-Log and Semilog Graph Paper 3-5 Residual Plots and Mathematical Models Eploration: Coffee Data Residual Plot 3-6 Chapter Review and Test vii Precalculus with Trigonometr Course Sampler 1

2 Chapter 4 Polnomial and Rational Functions Introduction to Polnomial and Rational Functions Quadratic Functions, Factoring, and Comple Numbers Graphs and Zeros of Higher-Degree Functions Eploration: Graphs and Zeros of Cubic Functions 4-4 Fitting Polnomial Functions to Data Rational Functions: Asmptotes and Discontinuities Eploration: Transformations of the Parent Reciprocal Function 4-6 Partial Fractions and Operations with Rational Epressions Fractional Equations and Etraneous Solutions Chapter Review and Test Cumulative Review, Chapters Unit 2 Trigonometric and Periodic Functions Chapter 5 Periodic Functions and Right Triangle Problems Introduction to Periodic Functions Measurement of Rotation Eploration: Reference Angles 5-3 Sine and Cosine Functions Values of the Si Trigonometric Functions Eploration: Values of the Sine and Cosine Functions 5-5 Inverse Trigonometric Functions and Triangle Problems Chapter Review and Test Chapter 6 Applications of Trigonometric and Circular Functions Sinusoids: Amplitude, Period, and Ccles General Sinusoidal Graphs Eploration: Periodic Dail Temperatures 6-3 Graphs of Tangent, Cotangent, Secant, and Cosecant Functions Radian Measure of Angles Eploration: Introduction to Radians 6-5 Circular Functions Inverse Circular Relations: Given, Find Sinusoidal Functions as Mathematical Models Eploration: Chemotherap Problem 6-8 Rotar Motion Eploration: Angular and Linear Velocit 6-9 Chapter Review and Test viii 2 Precalculus with Trigonometr Course Sampler

3 1 Chapter 7 Trigonometric Function Properties and Identities, and Parametric Functions Introduction to the Pthagorean Propert Pthagorean, Reciprocal, and Quotient Properties Eploration: Properties of Trigonometric Functions 7-3 Identities and Algebraic Transformation of Epressions Arcsine, Arctangent, Arccosine, and Trigonometric Equations Parametric Functions Eploration: Parametric Function Pendulum Problem 7-6 Inverse Trigonometric Relation Graphs Eploration: Graphs of Inverse Trigonometric Relations 7-7 Chapter Review and Test C b a A c B Chapter 8 Properties of Combined Sinusoids Introduction to Combinations of Sinusoids Composite Argument and Linear Combination Properties Eploration: Cosine of a Difference Discover 8-3 Other Composite Argument Properties Composition of Ordinates and Harmonic Analsis Eploration: Sum or Product of Sinusoids with Unequal Periods 8-5 The Sum and Product Properties Double and Half Argument Properties Chapter Review and Test Chapter 9 Triangle Trigonometr Introduction to Oblique Triangles Oblique Triangles: The Law of Cosines Eploration: Derivation of the Law of Cosines 9-3 Area of a Triangle Eploration: Area of a Triangle and Hero s Formula 9-4 Oblique Triangles: The Law of Sines Eploration: The Law of Sines 9-5 The Ambiguous Case Vector Addition Eploration: Sum of Two Displacement Vectors 9-7 Real-World Triangle Problems Chapter Review and Test Cumulative Review, Chapters i Precalculus with Trigonometr Course Sampler 3

4 Unit 3 Analtic Geometr Chapter 10 Conic Sections and Quadric Surfaces Quadratic Relations and Conic Sections Cartesian Equations for Conic Sections Parametric Equations for Conic Sections Eploration: Introduction to Parametric Equations for Conic Sections 10-4 Quadric Surfaces and Inscribed Figures Analtic Geometr of the Conic Sections Eploration: Focus, Directri, and Eccentricit of an Ellipse 10-6 Parametric and Cartesian Equations for Rotated Conics Eploration: Rotation of a Figure B Matri Multiplication 10-7 Applications of Conic Sections Chapter Review and Test Chapter 11 Polar Coordinates, Comple Numbers, and Moving Objects Introduction to Polar Coordinates Polar Equations for Conics and Other Curves Eploration: Limaçon in Polar Coordinates 11-3 Intersections of Polar Curves Eploration: Intersections of Polar Curves 11-4 Comple Numbers in Polar Form Eploration: Review of Comple Numbers 11-5 Parametric Equations for Moving Objects Chapter Review and Test z v Chapter 12 Three-Dimensional Vectors Review of Two-Dimensional Vectors Two-Dimensional Vector Practice Vectors in Space Eploration: Introduction to Three-Dimensional Vectors 12-4 Scalar Products and Projections of Vectors Planes in Space Vector Product of Two Vectors Eploration: Introduction to the Cross Product 12-7 Direction Angles and Direction Cosines Vector Equations for Lines in Space Chapter Review and Test Precalculus with Trigonometr Course Sampler

5 Chapter 13 Matri Transformations and Fractal Figures Introduction to Iterated Transformations Matri Operations and Solutions of Linear Sstems Eploration: Inverse of a 3 3 Matri 13-3 Rotation and Dilation Matrices Translation with Rotation and Dilation Matrices Eploration: Combined Translation, Rotation, and Dilation 13-5 Strange Attractors for Several Iterated Transformations Fractal Dimensions Chapter Review and Test Cumulative Review, Chapters P() Unit 4 Introduction to Discrete and Continuous Mathematics Chapter 14 Probabilit, and Functions of a Random Variable Introduction to Probabilit Words Associated with Probabilit Two Counting Principles Probabilities of Various Permutations Probabilities of Various Combinations Eploration: Reading about Combinations 14-6 Properties of Probabilit Functions of a Random Variable Mathematical Epectation Eploration: Mathematical Epectation 14-9 Chapter Review and Test t n n Chapter 15 Sequences and Series Introduction to Sequences and Series Arithmetic, Geometric, and Other Sequences Eploration: Patterns in Sequences 15-3 Series and Partial Sums Eploration: Introduction to Series 15-4 Chapter Review and Test i Precalculus with Trigonometr Course Sampler 5

6 f () Chapter 16 Introduction to Limits, Derivatives, and Integrals Eploring Limits, Derivatives, and Integrals Limits Eploration: Limits 16-3 Rate of Change of a Function: The Derivative Accumulated Rates: The Definite Integral Chapter Review and Test Cumulative Review, Chapters Appendi A Tpes of Numbers, Aioms, and Other Properties 823 Appendi B Mathematical Induction 833 Answers to Selected Problems 839 Glossar 937 Inde of Problem Titles 948 General Inde 954 Photograph Credits 971 ii 6 Precalculus with Trigonometr Course Sampler