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Preface | p. xii |
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 | |
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 | |
Analytic 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 |
Further Topics in Algebra | p. 565 |
Sequences and Series | p. 566 |
Sequences | |
Series and Summation Notation | |
Summation Properties | |
Arithmetic Sequences and Series | p. 576 |
Arithmetic Sequences | |
Arithmetic Series | |
Geometric Sequences and Series | p. 584 |
Geometric Sequences | |
Geometric Series | |
Infinite Geometric Series | |
Annuities | |
Reviewing Basic Concepts (Sections 8.1-8.3) | p. 594 |
The Binomial Theorem | p. 595 |
A Binomial Expansion Pattern | |
Pascal's Triangle | |
n-Factorial | |
Binomial Coefficients | |
The Binomial Theorem | |
rth Term of a Binomial Expansion | |
Mathematical Induction | p. 602 |
Proof by Mathematical Induction | |
Proving Statements | |
Generalized Principle of Mathematical Induction | |
Proof of the Binomial Theorem | |
Reviewing Basic Concepts (Sections 8.4 and 8.5) | p. 608 |
Counting Theory | p. 608 |
Fundamental Principle of Counting | |
Permutations | |
Combinations | |
Distinguishing between Permutations and Combinations | |
Probability | p. 617 |
Basic Concepts | |
Complements and Venn Diagrams | |
Odds | |
Union of Two Events | |
Binomial Probability | |
Reviewing Basic Concepts (Sections 8.6 and 8.7) | p. 626 |
Chapter 8 Summary | p. 627 |
Chapter 8 Review Exercises | p. 631 |
Chapter 8 Test | p. 633 |
Chapter 8 Project Using Experimental Probabilities to Simulate Family Makeup | p. 634 |
Reference: Basic Algebraic Concepts | p. 637 |
Review of Exponents and Polynomials | p. 638 |
Rules for Exponents | |
Terminology for Polynomials | |
Adding and Subtracting Polynomials | |
Multiplying Polynomials | |
Review of Factoring | p. 644 |
Factoring Out the Greatest Common Factor | |
Factoring by Grouping | |
Factoring Trinomials | |
Factoring Special Products | |
Factoring by Substitution | |
Review of Rational Expressions | p. 651 |
Domain of a Rational Expression | |
Lowest Terms of a Rational Expression | |
Multiplying and Dividing Rational Expressions | |
Adding and Subtracting Rational Expressions | |
Complex Fractions | |
Review of Negative and Rational Exponents | p. 659 |
Negative Exponents and the Quotient Rule | |
Rational Exponents | |
Review of Radicals | p. 665 |
Radical Notation | |
Rules for Radicals | |
Simplifying Radicals | |
Operations with Radicals | |
Rationalizing Denominators | |
Chapter R Test | p. 673 |
Geometry Formulas | p. 674 |
Deciding Which Model Best Fits a Set of Data | p. 676 |
Answers to Selected Exercises | p. 1 |
Index of Applications | p. 1 |
Index | p. 5 |
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