John Hornsby- When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics, education, or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, all three of his goals have been realized; his love for teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum.
John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.
Marge Lial has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College.
Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
Gary Rockswold- Dr. Gary Rockswold has been teaching mathematics for 33 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate, and graduate students, and adult education classes. He is currently employed at Minnesota State University, Mankato, where he is a full professor of mathematics. He graduated with majors in mathematics and physics from
Preface | p. xiv |
Linear Functions, Equations, and Inequalities | p. 1 |
Real Numbers and the Rectangular Coordinate System | p. 2 |
Sets of Real Numbers | |
The Rectangular Coordinate System | |
Viewing Windows | |
Roots | |
Distance and Midpoint Formulas | |
Introduction to Relations and Functions | p. 12 |
Set-Builder Notation and Interval Notation | |
Relations, Domain, and Range | |
Functions | |
Tables | |
Function Notation | |
Reviewing Basic Concepts (Sections 1.1 and 1.2) | p. 22 |
Linear Functions | p. 23 |
Basic Concepts about Linear Functions | |
Slope of a Line | |
Slope-Intercept Form of the Equation of a Line | |
Equations of Lines and Linear Models | p. 36 |
Point-Slope Form of the Equation of a Line | |
Standard Form of the Equation of a Line | |
Parallel and Perpendicular Lines | |
Linear Models and Regression | |
Reviewing Basic Concepts (Sections 1.3 and 1.4) | p. 50 |
Linear Equations and Inequalities | p. 51 |
Solving Linear Equations | |
Graphical Approaches to Solving Linear Equations | |
Identities and Contradictions | |
Solving Linear Inequalities | |
Graphical Approaches to Solving Linear Inequalities | |
Three-Part Inequalities | |
Applications of Linear Functions | p. 66 |
Problem-Solving Strategies | |
Applications of Linear Equations | |
Break-Even Analysis | |
Direct Variation | |
Formulas | |
Reviewing Basic Concepts (Sections 1.5 and 1.6) | p. 78 |
Chapter 1 Summary | p. 79 |
Chapter 1 Review Exercises | p. 82 |
Chapter 1 Test | p. 87 |
Chapter 1 Project: Predicting Heights and Weights of Athletes | p. 88 |
Analysis of Graphs of Functions | p. 89 |
Graphs of Basic Functions and Relations; Symmetry | p. 90 |
Continuity | |
Increasing and Decreasing Functions | |
The Identity Function | |
The Squaring Function and Symmetry with Respect to the y-Axis | |
The Cubing Function and Symmetry with Respect to the Origin | |
The Square Root and Cube Root Functions | |
The Absolute Value Function | |
The Relation x - y[superscript 2] and Symmetry with Respect to the x-Axis | |
Even and Odd Functions | |
Vertical and Horizontal Shifts of Graphs | p. 103 |
Vertical Shifts | |
Horizontal Shifts | |
Combinations of Vertical and Horizontal Shifts | |
Effects of Shifts on Domain and Range | |
Horizontal Shifts Applied to Equations for Modeling | |
Stretching, Shrinking, and Reflecting Graphs | p. 113 |
Vertical Stretching | |
Vertical Shrinking | |
Horizontal Stretching and Shrinking | |
Reflecting across an Axis | |
Combining Transformations of Graphs | |
Reviewing Basic Concepts (Sections 2.1-2.3) | p. 125 |
Absolute Value Functions: Graphs, Equations, Inequalities, and Applications | p. 127 |
The Graph of y = [vertical bar]f(x)[vertical bar] | |
Properties of Absolute Value | |
Equations and Inequalities Involving Absolute Value | |
An Application Involving Absolute Value | |
Piecewise-Defined Functions | p. 138 |
Graphing Piecewise-Defined Functions | |
The Greatest Integer Function | |
Applications of Piecewise-Defined Functions | |
Operations and Composition | p. 149 |
Operations on Functions | |
The Difference Quotient | |
Composition of Functions | |
Applications of Operations and Composition | |
Reviewing Basic Concepts (Sections 2.4-2.6) | p. 162 |
Chapter 2 Summary | p. 163 |
Chapter 2 Review Exercises | p. 166 |
Chapter 2 Test | p. 169 |
Chapter 2 Project: Modeling the Movement of a Cold Front | p. 171 |
Polynomial Functions | p. 173 |
Complex Numbers | p. 174 |
The Number i | |
Operations with Complex Numbers | p. 174 |
Quadratic Functions and Graphs | p. 181 |
Completing the Square | |
Graphs of Quadratic Functions | |
Vertex Formula | |
Extreme Values | |
Applications and Quadratic Models | |
Quadratic Equations and Inequalities | p. 194 |
Zero-Product Property | |
Solving x[superscript 2] = k | |
Quadratic Formula and the Discriminant | |
Solving Quadratic Equations | |
Solving Quadratic Inequalities | |
Formulas Involving Quadratics | |
Another Quadratic Model | |
Reviewing Basic Concepts (Sections 3.1-3.3) | p. 208 |
Further Applications of Quadratic Functions and Models | p. 208 |
Applications of Quadratic Functions | |
Quadratic Models | |
Higher-Degree Polynomial Functions and Graphs | p. 218 |
Cubic Functions | |
Quartic Functions | |
Extrema | |
End Behavior | |
x-Intercepts (Real Zeros) | |
Comprehensive Graphs | |
Curve Fitting and Polynomial Models | |
Reviewing Basic Concepts (Sections 3.4 and 3.5) | p. 231 |
Topics in the Theory of Polynomial Functions (I) | p. 231 |
Intermediate Value Theorem | |
Division of Polynomials and Synthetic Division | |
Remainder and Factor Theorems | |
Topics in the Theory of Polynomial Functions (II) | p. 240 |
Complex Zeros and the Fundamental Theorem of Algebra | |
Number of Zeros | |
Rational Zeros Theorem | |
Descartes' Rule of Signs | |
Boundedness Theorem | |
Polynomial Equations and Inequalities; Further Applications and Models | p. 251 |
Polynomial Equations and Inequalities | |
Complex nth Roots | |
Applications and Polynomial Models | |
Reviewing Basic Concepts (Sections 3.6-3.8) | p. 259 |
Chapter 3 Summary | p. 260 |
Chapter 3 Review Exercises | p. 263 |
Chapter 3 Test | p. 267 |
Chapter 3 Project: Creating a Social Security Polynomial | p. 268 |
Rational, Power, and Root Functions | p. 270 |
Rational Functions and Graphs | p. 271 |
The Reciprocal Function | |
The Rational Function Defined by f(x) = 1 / x[superscript 2] | |
More on Graphs of Rational Functions | p. 277 |
Vertical and Horizontal Asymptotes | |
Graphing Techniques | |
Oblique Asymptotes | |
Graphs with Points of Discontinuity | |
Rational Equations, Inequalities, Applications, and Models | p. 291 |
Solving Rational Equations and Inequalities | |
Applications and Models of Rational Functions | |
Inverse Variation | |
Combined and Joint Variation | |
Reviewing Basic Concepts (Sections 4.1-4.3) | p. 305 |
Functions Defined by Powers and Roots | p. 306 |
Power and Root Functions | |
Modeling Using Power Functions | |
Graphs of f(x) = [characters not reproducible] | |
Graphing Circles and Horizontal Parabolas Using Root Functions | |
Equations, Inequalities, and Applications Involving Root Functions | p. 318 |
Equations and Inequalities | |
An Application of Root Functions | |
Reviewing Basic Concepts (Sections 4.4 and 4.5) | p. 328 |
Chapter 4 Summary | p. 329 |
Chapter 4 Review Exercises | p. 331 |
Chapter 4 Test | p. 335 |
Chapter 4 Project: How Rugged Is Your Coastline? | p. 336 |
Inverse, Exponential, and Logarithmic Functions | p. 338 |
Inverse Functions | p. 339 |
Inverse Operations | |
One-to-One Functions | |
Inverse Functions and Their Graphs | |
Equations of Inverse Functions | |
An Application of Inverse Functions | |
Exponential Functions | p. 350 |
Real-Number Exponents | |
Graphs of Exponential Functions | |
Exponential Equations (Type 1) | |
Compound Interest | |
The Number e and Continuous Compounding | |
An Application of Exponential Functions | |
Logarithms and Their Properties | p. 363 |
Definition of Logarithm | |
Common Logarithms | |
Natural Logarithms | |
Properties of Logarithms | |
Change-of-Base Rule | |
Reviewing Basic Concepts (Sections 5.1-5.3) | p. 373 |
Logarithmic Functions | p. 374 |
Graphs of Logarithmic Functions | |
Applying Earlier Work to Logarithmic Functions | |
A Logarithmic Model | |
Exponential and Logarithmic Equations and Inequalities | p. 384 |
Exponential Equations and Inequalities (Type 2) | |
Logarithmic Equations and Inequalities | |
Equations and Inequalities Involving Both Exponentials and Logarithms | |
Formulas Involving Exponentials and Logarithms | |
Reviewing Basic Concepts (Sections 5.4 and 5.5) | p. 393 |
Further Applications and Modeling with Exponential and Logarithmic Functions | p. 394 |
Physical Science Applications | |
Financial Applications | |
Biological and Medical Applications | |
Modeling Data with Exponential and Logarithmic Functions | |
Chapter 5 Summary | p. 408 |
Chapter 5 Review Exercises | p. 411 |
Chapter 5 Test | p. 414 |
Chapter 5 Project: Modeling Motor Vehicle Sales in the United States (with a lesson about the careless use of mathematical models) | p. 415 |
Analytic Geometry | p. 417 |
Circles and Parabolas | p. 418 |
Conic Sections | |
Equations and Graphs of Circles | |
Equations and Graphs of Parabolas | |
Translations of Parabolas | |
An Application of Parabolas | |
Ellipses and Hyperbolas | p. 432 |
Equations and Graphs of Ellipses | |
Translations of Ellipses | |
An Application of Ellipses | |
Equations and Graphs of Hyperbolas | |
Translations of Hyperbolas | |
Reviewing Basic Concepts (Sections 6.1 and 6.2) | p. 445 |
Summary of the Conic Sections | p. 445 |
Characteristics | |
Identifying Conic Sections | |
Eccentricity | |
Parametric Equations | p. 454 |
Graphs of Parametric Equations and Their Rectangular Equivalents | |
Alternative Forms of Parametric Equations | |
An Application of Parametric Equations | |
Reviewing Basic Concepts (Sections 6.3 and 6.4) | p. 458 |
Chapter 6 Summary | p. 459 |
Chapter 6 Review Exercises | p. 461 |
Chapter 6 Test | p. 463 |
Chapter 6 Project: Modeling the Path of a Bouncing Ball | p. 464 |
Systems of Equations and Inequalities; Matrices | p. 466 |
Systems of Equations | p. 467 |
Linear Systems | |
Substitution Method | |
Elimination Method | |
Special Systems | |
Nonlinear Systems | |
Applications of Systems | |
Solution of Linear Systems in Three Variables | p. 480 |
Geometric Considerations | |
Analyttic Solution of Systems in Three Variables | |
Applications of Systems | |
Curve Fitting Using a System | |
Solution of Linear Systems by Row Transformations | p. 488 |
Matrix Row Transformations | |
Row Echelon Method | |
Reduced Row Echelon Method | |
Special Cases | |
An Application of Matrices | |
Reviewing Basic Concepts (Sections 7.1-7.3) | p. 499 |
Matrix Properties and Operations | p. 500 |
Terminology of Matrices | |
Operations on Matrices | |
Applying Matrix Algebra | |
Determinants and Cramer's Rule | p. 513 |
Determinants of 2 x 2 Matrices | |
Determinants of Larger Matrices | |
Derivation of Cramer's Rule | |
Using Cramer's Rule to Solve Systems | |
Solution of Linear Systems by Matrix Inverses | p. 524 |
Identity Matrices | |
Multiplicative Inverses of Square Matrices | |
Using Determinants to Find Inverses | |
Solving Linear Systems Using Inverse Matrices | |
Curve Fitting Using a System | |
Reviewing Basic Concepts (Sections 7.4-7.6) | p. 536 |
Systems of Inequalities and Linear Programming | p. 537 |
Solving Linear Inequalities | |
Solving Systems of Inequalities | |
Linear Programming | |
Partial Fractions | p. 547 |
Decomposition of Rational Expressions | |
Distinct Linear Factors | |
Repeated Linear Factors | |
Distinct Linear and Quadratic Factors | |
Repeated Quadratic Factors | |
Reviewing Basic Concepts (Sections 7.7 and 7.8) | p. 554 |
Chapter 7 Summary | p. 554 |
Chapter 7 Review Exercises | p. 557 |
Chapter 7 Test | p. 561 |
Chapter 7 Project: Finding a Polynomial Whose Graph Passes through Any Number of Given Points | p. 562 |
Trigonometric Functions and Applications | p. 565 |
Angles and Their Measures | p. 566 |
Basic Terminology | |
Degree Measure | |
Standard Position and Coterminal Angles | |
Radian Measure | |
Arc Lengths and Areas of Sectors | |
Angular and Linear Speed | |
Trigonometric Functions and Fundamental Identities | p. 582 |
Trigonometric Functions | |
Quadrantal Angles | |
Reciprocal Identities | |
Signs and Ranges of Function Values | |
Pythagorean Identities | |
Quotient Identities | |
An Application of Trigonometric Functions | |
Reviewing Basic Concepts (Sections 8.1 and 8.2) | p. 595 |
Evaluating Trigonometric Functions | p. 596 |
Definitions of the Trigonometric Functions | |
Trigonometric Function Values of Special Angles | |
Cofunction Identities | |
Reference Angles | |
Special Angles as Reference Angles | |
Finding Function Values with a Calculator | |
Finding Angle Measures | |
Applications of Right Triangles | p. 608 |
Significant Digits | |
Solving Triangles | |
Angles of Elevation or Depression | |
Bearing | |
Further Applications of Trigonometric Functions | |
Reviewing Basic Concepts (Sections 8.3 and 8.4) | p. 620 |
The Circular Functions | p. 620 |
Circular Functions | |
Applications of Circular Functions | |
Graphs of the Sine and Cosine Functions | p. 629 |
Periodic Functions | |
Graph of the Sine Function | |
Graph of the Cosine Function | |
Graphing Techniques, Amplitude, and Period | |
Translations | |
Determining a Trigonometric Model Using Curve Fitting | |
Reviewing Basic Concepts (Sections 8.5 and 8.6) | p. 646 |
Graphs of the Other Circular Functions | p. 646 |
Graphs of the Cosecant and Secant Functions | |
Graphs of the Tangent and Cotangent Functions | |
Addition of Ordinates | |
Harmonic Motion | p. 657 |
Simple Harmonic Motion | |
Damped Oscillatory Motion | |
Reviewing Basic Concepts (Sections 8.7 and 8.8) | p. 660 |
Chapter 8 Summary | p. 661 |
Chapter 8 Review Exercises | p. 665 |
Chapter 8 Test | p. 670 |
Chapter 8 Project: Modeling Sunset Times | p. 671 |
Trigonometric Identities and Equations | p. 672 |
Trigonometric Identities | p. 673 |
Fundamental Identities | |
Using the Fundamental Identities | |
Verifying Identities | |
Sum and Difference Identities | p. 683 |
Cosine Sum and Difference Identities | |
Sine and Tangent Sum and Difference Identities | |
Reviewing Basic Concepts (Sections 9.1 and 9.2) | p. 692 |
Further Identities | p. 692 |
Double-Number Identities | |
Product-to-Sum and Sum-to-Product Identities | |
Half-Number Identities | |
The Inverse Circular Functions | p. 704 |
Review of Inverse Functions | |
Inverse Sine Function | |
Inverse Cosine Function | |
Inverse Tangent Function | |
Remaining Inverse Trigonometric Functions | |
Inverse Function Values | |
Reviewing Basic Concepts (Sections 9.3 and 9.4) | p. 717 |
Trigonometric Equations and Inequalities (I) | p. 717 |
Equations Solvable by Linear Methods | |
Equations Solvable by Factoring | |
Equations Solvable by the Quadratic Formula | |
Using Trigonometric Identities to Solve Equations | |
Trigonometric Equations and Inequalities (II) | p. 724 |
Equations and Inequalities Involving Multiple-Number Identities | |
Equations and Inequalities Involving Half-Number Identities | |
An Application of Trigonometric Equations | |
Reviewing Basic Concepts (Sections 9.5 and 9.6) | p. 730 |
Chapter 9 Summary | p. 731 |
Chapter 9 Review Exercises | p. 733 |
Chapter 9 Test | p. 736 |
Chapter 9 Project: Modeling a Damped Pendulum | p. 737 |
Applications of Trigonometry; Vectors | p. 739 |
The Law of Sines | p. 740 |
Congruency and Oblique Triangles | |
Derivation of the Law of Sines | |
Applications of Triangles | |
Ambiguous Case | |
The Law of Cosines and Area Formulas | p. 754 |
Derivation of the Law of Cosines | |
Applications of Triangles | |
Area Formulas | |
Vectors and Their Applications | p. 764 |
Basic Terminology | |
Algebraic Interpretation of Vectors | |
Operations with Vectors | |
Dot Product and the Angle between Vectors | |
Applications of Vectors | |
Reviewing Basic Concepts (Sections 10.1-10.3) | p. 777 |
Trigonometric (Polar) Form of Complex Numbers | p. 778 |
The Complex Plane and Vector Representation | |
Trigonometric (Polar) Form | |
Products of Complex Numbers in Trigonometric Form | |
Quotients of Complex Numbers in Trigonometric Form | |
Powers and Roots of Complex Numbers | p. 787 |
Powers of Complex Numbers (De Moivre's Theorem) | |
Roots of Complex Numbers | |
Reviewing Basic Concepts (Sections 10.4 and 10.5) | p. 793 |
Polar Equations and Graphs | p. 793 |
Polar Coordinate System | |
Graphs of Polar Equations | |
Classifying Polar Equations | |
Converting Equations | |
More Parametric Equations | p. 804 |
Parametric Equations with Trigonometric Functions | |
The Cycloid | |
Applications of Parametric Equations | |
Reviewing Basic Concepts (Sections 10.6 and 10.7) | p. 811 |
Chapter 10 Summary | p. 811 |
Chapter 10 Review Exercises | p. 814 |
Chapter 10 Test | p. 817 |
Chapter 10 Project: When Is a Circle Really a Polygon? | p. 818 |
Further Topics in Algebra | p. 820 |
Sequences and Series | p. 821 |
Sequences | |
Series and Summation Notation | |
Summation Properties | |
Arithmetic Sequences and Series | p. 831 |
Arithmetic Sequences | |
Arithmetic Series | |
Geometric Sequences and Series | p. 839 |
Geometric Sequences | |
Geometric Series | |
Infinite Geometric Series | |
Annuities | |
Reviewing Basic Concepts (Sections 11.1-11.3) | p. 849 |
The Binomial Theorem | p. 850 |
A Binomial Expansion Pattern | |
Pascal's Triangle | |
n-Factorial | |
Binomial Coefficients | |
The Binomial Theorem | |
rth Term of a Binomial Expansion | |
Mathematical Induction | p. 857 |
Proof by Mathematical Induction | |
Proving Statements | |
Generalized Principle of Mathematical Induction | |
Proof of the Binomial Theorem | |
Reviewing Basic Concepts (Sections 11.4 and 11.5) | p. 863 |
Counting Theory | p. 863 |
Fundamental Principle of Counting | |
Permutations | |
Combinations | |
Distinguishing between Permutations and Combinations | |
Probability | p. 872 |
Basic Concepts | |
Complements and Venn Diagrams | |
Odds | |
Union of Two Events | |
Binomial Probability | |
Reviewing Basic Concepts (Sections 11.6 and 11.7) | p. 881 |
Chapter 11 Summary | p. 882 |
Chapter 11 Review Exercises | p. 886 |
Chapter 11 Test | p. 888 |
Chapter 11 Project: Using Experimental Probabilities to Simulate Family Makeup | p. 889 |
Reference: Basic Algebraic Concepts | p. 892 |
Review of Exponents and Polynomials | p. 893 |
Rules for Exponents | |
Terminology for Polynomials | |
Adding and Subtracting Polynomials | |
Multiplying Polynomials | |
Review of Factoring | p. 899 |
Factoring Out the Greatest Common Factor | |
Factoring by Grouping | |
Factoring Trinomials | |
Factoring Special Products | |
Factoring by Substitution | |
Review of Rational Expressions | p. 906 |
Domain of a Rational Expression | |
Lowest Terms of a Rational Expression | |
Multipling and Dividing Rational Expressions | |
Adding and Subtracting Rational Expressions | |
Complex Fractions | |
Review of Negative and Rational Exponents | p. 914 |
Negative Exponents and the Quotient Rule | |
Rational Exponents | |
Review of Radicals | p. 920 |
Radical Notation | |
Rules for Radicals | |
Simplifying Radicals | |
Operations with Radicals | |
Rationalizing Denominators | |
Chapter R Test | p. 928 |
Geometry Formulas | p. 929 |
Deciding Which Model Best Fits a Set of Data | p. 931 |
Vectors in Space | p. 936 |
Polar Form of Conic Sections | p. 942 |
Rotation of Axes | p. 946 |
Answers to Selected Exercises | p. 1 |
Index of Applications | p. 1 |
Index | p. 5 |
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