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Experiencing Introductory and Intermediate Algebra

by ;
Edition:
2nd
ISBN13:

9780130356826

ISBN10:
0130356824
Format:
Hardcover
Pub. Date:
1/1/2003
Publisher(s):
Prentice Hall

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Summary

This book bridges the gap between traditional algebra texts and reform texts, written to promote the AMATYC standards published as Crossroads in Mathematics. It provides users with a sound traditional mathematical foundation, fully integrates graphing calculator technology, and encourages computer activities. This book includes key topics in algebra such as linear equations and inequalities with one variable, systems of equations, polynomial functions and equations, quadratic functions and equations, exponential functions and equations, logarithmic functions an equations, and rational and radical expressions. For professionals who wish to brush up on their algebra skills or enhance them with the use of graphing calculators and computers.

Table of Contents

Preface xi
Real Numbers
1(94)
Rational Numbers and the Number Line
2(13)
Addition and Subtraction
15(13)
Multiplication and Division
28(16)
Exponents and Roots
44(16)
Scientific Notation
60(10)
Properties of Real Numbers and Order of Operations
70(25)
Chapter Summary
80(1)
Section-by-Section Review
81(8)
Chapter Review
89(2)
Chapter Test
91(2)
Chapter Project
93(2)
Variables, Expressions, Equations, and Formulas
95(48)
Variables and Algebraic Expressions
96(7)
Simplifying Algebraic Expressions
103(9)
Equations
112(8)
Formulas
120(23)
Chapter Summary
133(1)
Section-by-Section Review
133(4)
Chapter Review
137(2)
Chapter Test
139(1)
Chapter Project
140(3)
Relations, Functions, and Graphs
143(74)
Tables of Values, Ordered Pairs, and Relations
144(11)
Rectangular Coordinate System and Graphing
155(19)
Functions and Function Notation
174(10)
Analyzing Graphs
184(33)
Chapter Summary
200(1)
Section-by-Section Review
200(8)
Chapter Review
208(2)
Chapter Test
210(2)
Chapter Project
212(2)
Chapter 1-3 Cumulative Review
214(3)
Linear Equations in One Varible
217(82)
Solving Equations Numerically and Graphically
218(17)
Solving Equations by Using Addition and Multiplication
235(11)
Solving Equations by Using a Combination of Properties
246(12)
Solving Equations or Formulas for a Specified Variable
258(8)
More Real-World Models
266(10)
Solving Linear Absolute-Value Equations
276(23)
Chapter Summary
286(1)
Section-by-Section Review
286(6)
Chapter Review
292(2)
Chapter Test
294(1)
Chapter Project
295(4)
Linear Equations and Functions
299(86)
Graphing by Using Ordered Pairs
300(18)
Graphing by Using the Slope-Intercept Method
318(22)
Coinciding, Parallel, and Perpendicular Lines
340(11)
Writing Linear Equations from Given Data
351(34)
Chapter Summary
367(1)
Section-by-Section Review
368(6)
Chapter Review
374(3)
Chapter Test
377(2)
Chapter Project
379(3)
Chapter 1--5 Cumulative Review
382(3)
Systems of Linear Equations
385(76)
Solving Systems of Two Equations Graphically
386(12)
Solving Systems of Two Equations by Using Substitution
398(11)
Solving Systems of Two Equations by Using Elimination
409(12)
More Real-World Models
421(14)
Solving Systems of Linear Equations in Three Variables
435(26)
Chapter Summary
448(1)
Section-by-Section Review
448(6)
Chapter Review
454(2)
Chapter Test
456(2)
Chapter Project
458(3)
Linear Inequalities
461(70)
Introduction to Linear Inequalities
462(12)
Linear Inequalities in One Variable
474(16)
Linear Inequalities in Two Variables
490(15)
Systems of Linear Inequalities in Two Variables
505(26)
Chapter Summary
517(1)
Section-by-Section Review
518(5)
Chapter Review
523(2)
Chapter Test
525(2)
Chapter Project
527(1)
Chapter 1-7 Cumulative Review
528(3)
Polynomial Functions
531(62)
Introduction to Polynomials
532(10)
Polynomial Functions and Their Graphs
542(13)
Quadratic Functions and Their Graphs
555(14)
Writing Quadratic Functions
569(24)
Chapter Summary
571(9)
Section-by-Section Review
580(6)
Chapter Review
586(2)
Chapter Test
588(2)
Chapter Project
590(3)
Exponents and Polynomials
593(56)
Operations Involving Nonnegative Exponents
594(12)
Operations Involving Negative Exponents
606(8)
Polynomial Addition and Subtraction
614(6)
Polynomial Multiplication
620(10)
Polynomial Division
630(19)
Chapter Summary
639(1)
Section-by-Section Review
639(4)
Chapter Review
643(2)
Chapter Test
645(1)
Chapter Project
646(3)
Factoring
649(58)
Greatest Common Factors
650(12)
Factoring Perfect-Square Trinomials, Differences of Squares, and Sums and Differences of Cubes
662(8)
Factoring Trinomials by Using the Trial-and-Error Method
670(13)
Factoring Trinomials by Using the Grouping Method
683(8)
General Strategies for Factoring
691(16)
Chapter Summary
698(1)
Section-by-Section Review
699(3)
Chapter Review
702(1)
Chapter Test
703(1)
Chapter Project
704(3)
Quadratic and Other Polynomial Equations and Inequalities
707(92)
Solving Equations Numerically and Graphically
708(11)
Solving Equations Algebraically by Factoring
719(10)
Solving Quadratic Equations by Using Square Roots
729(12)
Solving Quadratic Equations by Completing the Square
741(8)
Solving Quadratic Equations by Using the Quadratic Formula
749(12)
More Real-World Models
761(8)
Solving Quadratic Inequalities
769(30)
Chapter Summary
784(1)
Section-by-Section Review
784(7)
Chapter Review
791(2)
Chapter Test
793(1)
Chapter Project
794(3)
Chapters 1--11 Cumulative Review
797(2)
Rational Expressions, Functions, and Equations
799(78)
Rational Expressions and Functions
800(15)
Multiplication and Division of Rational Expressions
815(12)
Addition and Substraction of Rational Expressions
827(16)
Solving Rational Equations in One Variable
843(12)
More Real-World Models
855(22)
Chapter Summary
865(1)
Section-by-Section Review
865(6)
Chapter Review
871(2)
Chapter Test
873(1)
Chapter Project
874(3)
Radical Expressions, Functions, and Equations
877(96)
Radical Expressions, Functions, and Graphs
878(13)
Rational Exponents
891(11)
Properties of Rational Exponents
902(7)
Properties of Radicals
909(11)
Operations on Radicals
920(8)
Solving Radical Equations in One Variable
928(12)
Equations with Imaginary-Number Solutions
940(33)
Chapter Summary
956(1)
Section-by-Section Review
957(7)
Chapter Review
964(2)
Chapter Test
966(2)
Chapter Project
968(2)
Chapter 1--13 Cumulative Review
970(3)
Exponential and Logarthmic Functions and Equations
973(67)
Inverse Functions
974(12)
Exponential Functions
986(11)
Logarithmic Functions
997(13)
Properties of Logarithms
1010(6)
Solving Exponential and Logarithmic Equations
1016(24)
Chapter Summary
1027(1)
Section-by-Section Review
1027(6)
Chapter Review
1033(2)
Chapter Test
1035(1)
Chapter Project
1036(2)
Chapter 1--14 Cumulative Review
1038(2)
Photo Credits 1040
Selected Answers 1(1)
Index 1

Excerpts

The second edition ofExperiencing Introductory and Intermediate Algebracontinues to embrace the goal of promoting a new approach to teaching and learning developmental mathematics. This approach combines a traditional model with the reform movements presented in the National Council of Teachers of Mathematics (NCTM) standards and the American Mathematical Association of Two-Year Colleges (AMATYC) standards. The NCTM goals state that in our present technological society, students should learn to value mathematics, reason and communicate mathematically, become confident of their mathematical abilities, and become mathematical problem solvers. The AMATYC standards for intellectual development state that students will model real-world situations, connect mathematics with other disciplines, and use appropriate technology. In this second edition, we have incorporated recommendations and suggestions from instructors and reviewers of the text. Instructors who currently use the text valued the real-world application feature and encouraged us to expand it. At the same time, they recommended that the text be streamlined to reduce its volume. The contents of this edition are still organized by families of functions, according to the AMATYC standards. Consequently, the first seven chapters of the text focus on linear expressions, equations, and functions. The next four chapters, Chapters 8 through 11, focus on polynomial expressions, equations, and functions. Chapter 12 presents rational expressions, equations, and functions, Chapter 13 examines radical expressions, equations, and functions, and Chapter 14 features exponential and logarithmic expressions, equations, and functions. We have condensed the discussion of the real-number system into a review of pre-algebra numeric topics that may be taught as a whole or by sections of choice. We have combined Chapters 1 and 2 of the previous edition into one chapter, postponing the discussion of rational exponents to a later chapter. Also, the coverage of radicals in the combined chapter is limited to square roots and cube roots. In the previous edition, exponents and polynomials were presented together with factoring, all within one chapter. We have now separated this material into two chapters. The first of the two, Chapter 9, focuses on exponents and polynomial operations. We have added a separate section on polynomial division that outlines polynomial long division in greater detail. Feedback from reviewers indicated a need for expanding and strengthening the discussion of factoring, so we have created a separate chapter on the subject, Chapter 10. In this new chapter, we offer more examples, more exercises, and a different ordering of topics. In the previous edition, there was a separate chapter on complex numbers. In this edition, complex numbers and equations with imaginary solutions have been placed at the end of Chapter 13, following the discussion of radical expressions, equations, and functions. We believe that that is the appropriate place for complex numbers for two major reasons: students will have just learned the algebra of radicals, and the new location provides a perfect opportunity to revisit the quadratic formula, thereby reinforcing their understanding of the concept. However, the section on complex numbers and equations with imaginary solutions has been written as a stand-alone section, and if an instructor so chooses, it could be presented after the discussion of the quadratic formula in Chapter 11. The first half of the text presents a balanced discussion of algebraic, numerical, and graphical methods for solving linear equations, so that students have a solid understanding of what the concepts represent. In the second half, the discussion of polynomial equations continues to utilize the same algebraic, numerical, and graphical techniques. This approach provides an opportunity for students who enter the sequence at that late point t


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