Investigating College Algebra with Technology

Annotated Contents vii Preface xix To the Student xxvii To the Instructor xxix Acknowledgments xxxi Chapter 1: Problem Solving 1 1.1 Pictures, Graphs, and Diagrams 2 1.2 Symbolic Representation 9 1.3 Organizing Information 16 1.4 Measures of Central Tendency and Box Plots 24 1.5 Measures of Spread 31 Chapter 1 Review 45 Chapter 2: Patterns and Recursion 53 2.1 Recursively Defined Sequences 54 2.2 Modeling Growth and Decay 64 2.3 A First Look at Limits 71 2.4 Graphing and Sequences 77 2.5 Loans and Investments 86 Chapter 2 Review 99 Chapter 3: Linear Models and Systems 103 3.1 Linear Equations 104 3.2 Revisiting Slope 111 3.3 Fitting a Line to Data 119 3.4 Linear Systems 127 3.5 Substitution and Elimination 133 Chapter 3 Review 142 Chapter 4: Functions, Relations, and Transformations 148 4.1 Interpreting Graphs 149 4.2 Function Notation 155 4.3 Lines in Motion 163 4.4 Translations and the Quadratic Family 170 4.5 Reflections and the Square Root Family 177 4.6 Stretches and Shrinks and the Absolute Value Family 184 4.7 Transformations and the Circle Family 192 4.8 Compositions of Functions 200 Chapter 4 Review 211 Chapter 5: Exponential, Power, and Logarithmic Functions 215 5.1 The Exponential Function 216 5.2 Properties of Exponents 223 5.3 Fractional Exponents and Roots 229 5.4 Applications of Power Equations 239 5.5 Building Inverses of Functions 243 5.6 The Logarithmic Function 251 5.7 Properties of Logarithms 257 5.8 Applications of Logarithms 264 Chapter 5 Review 273 Chapter 6: Quadratic and Other Polynomial Functions 277 6.1 Polynomial Degree and Finite Differences 278 6.2 Equivalent Quadratic Forms 286 6.3 Completing the Square 294 6.4 The Quadratic Formula 301 6.5 Complex Numbers 307 6.6 Factoring Polynomials 314 6.7 Higher-Degree Polynomials 320 6.8 More about Finding Solutions 327 Chapter 6 Review 337 Chapter 7: Matrices and Linear Systems 341 7.1 Matrix Representations 342 7.2 Matrix Operations 349 7.3 The Row Reduction Method 360 7.4 Solving Systems with Inverse Matrices 368 7.5 Systems of Linear Inequalities 378 7.6 Linear Programming 385 Chapter 7 Review 395 Chapter 8: Parametric Equations and Trigonometry 401 8.1 Graphing Parametric Equations 402 8.2 Converting Parametric to Nonparametric Equations 411 8.3 Right Triangle Trigonometry 418 8.4 Using Trigonometry to Set a Course 431 8.5 Projectile Motion 438 8.6 The Law of Sines 445 8.7 The Law of Cosines 453 Chapter 8 Review 462 Chapter 9: Conic Sections and Rational Functions 466 9.1 Using the Distance Formula 467 9.2 Circles and Ellipses 474 9.3 Parabolas 486 9.4 The Hyperbola 494 9.5 Nonlinear Systems of Equations 503 9.6 Introduction to Rational Functions 508 9.7 Graphs of Rational Functions 516 9.8 Operations with Rational Expressions 524 Chapter 9 Review 533 Chapter 10: Series 539 10.1 Arithmetic Series 540 10.2 Infinite Geometric Series 547 10.3 Partial Sums of Geometric Series 554 Chapter 10 Review 562 Chapter 11: Probability 565 11.1 Randomness and Probability 566 11.2 Counting Outcomes and Tree Diagrams 577 11.3 Mutually Exclusive Events and Venn Diagrams 586 11.4 Random Variables and Expected Value 593 11.5 Permutations and Probability 600 11.6 Combinations and Probability 607 11.7 The Binomial Theorem and Pascal's Triangle 613 Chapter 11 Review 623 Selected Answers 627 Glossary 675 Photo Credits 687 Index 688 Resources on the Student CD Prerequisite Review: Numbers and Figures * Operations on Numbers * The Ideas that Motivate Algebra * Exponents * Radicals * Polynomials * Factoring Polynomials * Rational Expressions Calculator Notes Microsoft(R) Excel Notes Interactive Spreadsheets for Excel Explorations