Preface to the Instructor | p. xiii |
List of Applications | p. xix |
Photo Credits | p. xxiii |
To the Student | p. xxiv |
Foundations: A Prelude To Functions | p. 1 |
The Distance and Midpoint Formulas | p. 2 |
Graphs of Equations in Two Variables; Intercepts; Symmetry | p. 8 |
Lines | p. 18 |
Circles | p. 33 |
Functions and Their Graphs | p. 39 |
Functions | p. 40 |
The Graph of a Function | p. 54 |
Properties of Functions | p. 63 |
Library of Functions; Piecewise-defined Functions | p. 75 |
Graphing Techniques: Transformations | p. 85 |
Mathematical Models: Constructing Functions | p. 97 |
Chapter Review | p. 105 |
Chapter Test | p. 111 |
Chapter Projects | p. 112 |
Linear and Quadratic Functions | p. 113 |
Properties of Linear Functions | p. 114 |
Building Linear Functions from Data; Direct Variation | p. 125 |
Quadratic Functions and Their Zeros | p. 133 |
Properties of Quadratic Functions | p. 144 |
Inequalities Involving Quadratic Functions | p. 154 |
Quadratic Models | p. 158 |
Complex Zeros of a Quadratic Function | p. 167 |
Equations and Inequalities Involving the Absolute Value Function | p. 170 |
Chapter Review | p. 175 |
Chapter Test | p. 179 |
Chapter Projects | p. 179 |
Cumulative Review | p. 180 |
Polynomial and Rational Functions | p. 181 |
Polynomial Functions and Models | p. 182 |
Properties of Rational Functions | p. 203 |
The Graph of a Rational Function; Inverse and Joint Variation | p. 213 |
Polynomial and Rational Inequalities | p. 231 |
The Real Zeros of a Polynomial Function | p. 236 |
Complex Zeros; Fundamental Theorem of Algebra | p. 250 |
Chapter Review | p. 256 |
Chapter Test | p. 259 |
Chapter Projects | p. 260 |
Cumulative Review | p. 261 |
Exponential and Logarithmic Functions | p. 263 |
Composite Functions | p. 264 |
One-to-One Functions; Inverse Functions | p. 271 |
Exponential Functions | p. 284 |
Logarithmic Functions | p. 300 |
Properties of Logarithms | p. 312 |
Logarithmic and Exponential Equations | p. 320 |
Compound Interest | p. 325 |
Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay | p. 334 |
Building Exponential, Logarithmic, and Logistic Functions from Data | p. 345 |
Chapter Review | p. 353 |
Chapter Test | p. 359 |
Chapter Projects | p. 359 |
Cumulative Review | p. 360 |
Trigonometric Functions | p. 361 |
Angles and Their Measure | p. 362 |
Right Triangle Trigonometry | p. 375 |
Computing the Values of Trigonometric Functions of Acute Angles | p. 386 |
Trigonometric Functions of General Angles | p. 397 |
Unit Circle Approach; Properties of the Trigonometric Functions | p. 407 |
Graphs of the Sine and Cosine Functions | p. 418 |
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions | p. 433 |
Phase Shift; Sinusoidal Curve Fitting | p. 439 |
Chapter Review | p. 450 |
Chapter Test | p. 456 |
Chapter Projects | p. 457 |
Cumulative Review | p. 458 |
Analytic Trigonometry | p. 459 |
The Inverse Sine, Cosine, and Tangent Functions | p. 460 |
The Inverse Trigonometric Functions (Continued) | p. 472 |
Trigonometric Identities | p. 477 |
Sum and Difference Formulas | p. 485 |
Double-angle and Half-angle Formulas | p. 494 |
Product-to-Sum and Sum-to-Product Formulas | p. 503 |
Trigonometric Equations (I) | p. 507 |
Trigonometric Equations (II) | p. 613 |
Chapter Review | p. 520 |
Chapter Test | p. 524 |
Chapter Projects | p. 524 |
Cumulative Review | p. 525 |
Applications of Trigonometric Functions | p. 527 |
Applications Involving Right Triangles | p. 528 |
The Law of Sines | p. 533 |
The Law of Cosines | p. 544 |
Area of a Triangle | p. 550 |
Simple Harmonic Motion; Damped Motion; Combining Waves | p. 555 |
Chapter Review | p. 564 |
Chapter Test | p. 568 |
Chapter Projects | p. 569 |
Cumulative Review | p. 570 |
Polar Coordinates; Vectors | p. 571 |
Polar Coordinates | p. 572 |
Polar Equations and Graphs | p. 580 |
The Complex Plane; De Moivre's Theorem | p. 596 |
Vectors | p. 604 |
The Dot Product | p. 615 |
Vectors in Space | p. 623 |
The Cross Product | p. 632 |
Chapter Review | p. 638 |
Chapter Test | p. 642 |
Chapter Projects | p. 643 |
Cumulative Review | p. 644 |
Analytic Geometry | p. 645 |
Conics | p. 646 |
The Parabola | p. 647 |
The Ellipse | p. 656 |
The Hyperbola | p. 666 |
Rotation of Axes; General Form of a Conic | p. 678 |
Polar Equations of Conics | p. 686 |
Plane Curves and Parametric Equations | p. 692 |
Chapter Review | p. 704 |
Chapter Test | p. 707 |
Chapter Projects | p. 707 |
Cumulative Review | p. 708 |
Systems of Equations and Inequalities | p. 709 |
Systems of Linear Equations: Substitution and Elimination | p. 710 |
Systems of Linear Equations: Matrices | p. 724 |
Systems of Linear Equations: Determinants | p. 739 |
Matrix Algebra | p. 749 |
Partial Fraction Decomposition | p. 765 |
Systems of Nonlinear Equations | p. 772 |
Systems of Inequalities | p. 781 |
Linear Programming | p. 789 |
Chapter Review | p. 796 |
Chapter Test | p. 801 |
Chapter Projects | p. 802 |
Cumulative Review | p. 803 |
Sequences; Induction; The Binomial Theorem | p. 805 |
Sequences | p. 806 |
Arithmetic Sequences | p. 815 |
Geometric Sequences; Geometric Series | p. 820 |
Mathematical Induction | p. 831 |
The Binomial Theorem | p. 834 |
Chapter Review | p. 841 |
Chapter Test | p. 843 |
Chapter Projects | p. 844 |
Cumulative Review | p. 844 |
Counting and Probability | p. 895 |
Sets and Counting | p. 846 |
Permutations and Combinations | p. 851 |
Probability | p. 861 |
Chapter Review | p. 871 |
Chapter Test | p. 874 |
Chapter Projects | p. 875 |
Cumulative Review | p. 875 |
A Preview of Calculus: The Limit, Derivative, and Integral of a Function | p. 877 |
Finding Limits Using Tables and Graphs | p. 878 |
Algebra Techniques for Finding Limits | p. 883 |
One-sided Limits; Continuous Functions | p. 890 |
The Tangent Problem; The Derivative | p. 897 |
The Area Problem; The Integral | p. 905 |
Chapter Review | p. 911 |
Chapter Test | p. 915 |
Chapter Projects | p. 916 |
Review | p. 1 |
Algebra Essentials | p. 1 |
Geometry Essentials | p. 11 |
Polynomials | p. 19 |
Factoring Polynomials | p. 29 |
Synthetic Division | p. 38 |
Rational Expressions | p. 41 |
nth Roots; Rational Exponents | p. 52 |
Solving Equations | p. 60 |
Interval Notation; Solving Inequalities | p. 66 |
Problem Solving: Applications of Linear Equations | p. 74 |
Complex Numbers | p. 82 |
Graphing Utilities | p. 1 |
The Viewing Rectangle | p. 1 |
Using a Graphing Utility to Graph Equations | p. 3 |
Using a Graphing Utility to Locate Intercepts and Check for Symmetry | p. 7 |
Using a Graphing Utility to Solve Equations | p. 9 |
Square Screens | p. 11 |
Using a Graphing Utility to Graph Inequalities | p. 12 |
Using a Graphing Utility to Solve Systems of Linear Equations | p. 14 |
Using a Graphing Utility to Graph a Polar Equation | p. 15 |
Using a Graphing Utility to Graph Parametric Equations | p. 16 |
Answers | p. 1 |
Index | p. 1 |
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