Graphical Approach to College Algebra, A

by Hornsby, John; Lial, Margaret L.; Rockswold, Gary K.

• ISBN13: 9780321356895
• ISBN10: 0321356896
• Edition: 4th
• Format: Hardcover
• Copyright: 2007-01-01
• Publisher: Addison Wesley

Summary

This edition has evolved to address the needs of today's student. While maintaining its unique table of contents and functions-based approach, the text now includes additional components to build skill, address critical thinking, solve applications, and apply technology to support traditional algebraic solutions. It continues to incorporate an open design, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids to provide new and relevant opportunities for learning and teaching.

Table of Contents

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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