Experiencing Introductory and Intermediate Algebra

9780130356826

0130356824

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