College Algebra: Graphs and Models

by Barnett, Raymond; Ziegler, Michael; Byleen, Karl; Sobecki, David

• ISBN13: 9780077221287
• ISBN10: 0077221281
• Edition: 3rd
• Format: Hardcover
• Copyright: 2008-02-01
• Publisher: McGraw Hill

Summary

TheBarnett Graphs & Modelsseries in college algebra and precalculus maximizes student comprehension by emphasizing computational skills, real-world data analysis and modeling, and problem solving rather than mathematical theory. Many examples feature side-by-side algebraic and graphical solutions, and each is followed by a matched problem for the student to work. This active involvement in the learning process helps students develop a more thorough understanding of concepts and processes.A hallmark of the Barnett series, the function concept serves as a unifying theme. A major objective of this book is to develop a library of elementary functions, including their important properties and uses. Employing this library as a basic working tool, students will be able to proceed through this course with greater confidence and understanding as they first learn to recognize the graph of a function and then learn to analyze the graph and use it to solve the problem. Applications included throughout the text give the student substantial experience in solving and modeling real world problems in an effort to convince even the most skeptical student that mathematics is really useful.

Table of Contents

Preface	p. vii
Application Index	p. xvi
Functions, Graphs, and Models	p. 1
Using Graphing Calculators	p. 2
Functions	p. 21
Functions: Graphs and Properties	p. 46
Functions: Graphs and Transformation	p. 67
Operations on Functions; Composition	p. 84
Inverse Functions	p. 99
Chapter 1 Review	p. 119
Chapter 1 Group Activity: Mathematical Modeling: Choosing a Cell Phone Provider	p. 126
Modeling with Linear and Quadratic Functions	p. 127
Linear Functions	p. 128
Linear Equations and Models	p. 151
Quadratic Functions	p. 172
Complex Numbers	p. 190
Quadratic Equations and Models	p. 206
Additional Equation-Solving Techniques	p. 226
Solving Inequalities	p. 241
Chapter 2 Review	p. 258
Chapter 2 Group Activity: Mathematical
Modeling in Population Studies	p. 265
Cumulative Review Exercises Chapter 1-2	p. 267
Polynomial and Rational Functions	p. 273
Polynomial Functions and Models	p. 274
Polynomial Division	p. 291
Real Zeros and Polynomial Inequalities	p. 303
Complex Zeros and Rational Zeros of Polynomials	p. 320
Rational Functions and Inequalities	p. 336
Variation and Modeling	p. 361
Chapter 3 Review	p. 371
Chapter 3 Group Activity: Interpolating Polynomials	p. 378
Exponential and Logarithmic Functions	p. 381
Exponential Functions	p. 382
Exponential Models	p. 399
Logarithmic Functions	p. 416
Logarithmic Models	p. 430
Exponential and Logarithmic Equations	p. 440
Chapter 4 Review	p. 462
Chapter 4 Group Activity: Comparing Regression Models	p. 456
Cumulative Review Exercises Chapter 3-4	p. 457
Modeling with Systems of Equations and Inequalities	p. 463
Systems of Linear Equations in Two Variables	p. 464
Systems of Linear Equations in Three Variables	p. 482
Systems of Linear Inequalities	p. 495
Linear Programming	p. 510
Chapter 5 Review	p. 522
Chapter 5 Group Activity: Heat Conduction	p. 526
Matrices and Determinants	p. 527
Systems of Linear Equations: Gauss-Jordan Elimination	p. 528
Matrix Operations	p. 547
Inverse of a Square Matrix	p. 565
Matrix Equations and Systems of Linear Equations	p. 578
Determinants	p. 588
Properties of Determinants	p. 597
Determinants and Cramer's Rule	p. 604
Chapter 6 Review	p. 610
Chapter 6 Group Activity: Using Matrices to Find Cost, Revenue, and Profit	p. 616
Cumulative Review Exercises Chapter 5-6	p. 618
Sequences, Induction, and Probability	p. 621
Sequences and Series	p. 622
Mathematical Induction	p. 633
Arithmetic and Geometric Sequences	p. 644
The Multiplication Principle, Permutations, and Combinations	p. 659
Sample Spaces and Probability	p. 676
The Binomial Formula	p. 696
Chapter 7 Review	p. 704
Chapter 7 Group Activity: Sequences Specified by Recursion Formulas	p. 709
Additional Topics in Analytic Geometry	p. 711
Conic Sections; Parabola	p. 712
Ellipse	p. 723
Hyperbola	p. 735
Systems of Nonlinear Equations	p. 750
Chapter 8 Review	p. 761
Chapter 8 Group Activity: Focal Chords	p. 765
Cumulative Review Exercises Chapter 7-8	p. 766
Basic Algebra Review	p. A-1
Algebra and Real Numbers	p. A-2
Exponents	p. A-13
Radicals	p. A-27
Polynomials: Basic Operations	p. A-36
Polynomials: Factoring	p. A-47
Rational Expressions: Basic Operations	p. A-58
Review *
Group Activity: Rational and Irrational Numbers *
*Available online at www.mhhe.com/barnett
Review of Equations and Graphing	p. A-69
Linear Equations and Inequalities	p. A-70
Cartesian Coordinate System	p. A-82
Basic Formulas in Analytic Geometry	p. A-91
Special Topics	p. A-105
Significant Digits	p. A-106
Partial Fractions	p. A-109
Descartes' Rule of Signs	p. A-118
Parametric Equations *
*Available online at www.mhhe.com/barnett
Geometric Formulas	p. A-123
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