Synopsis
Mathematical reform is the driving force behind the organization and development of this new precalculus text. The use of technology, primarily graphing utilities, is assumed throughout the text. The development of each topic proceeds from the concrete to the abstract and takes full advantage of technology, wherever appropriate. The first major objective of this book is to encourage students to investigate mathematical ideas and processes graphically and numerically, as well as algebraically. Proceeding in this way, students gain a broader, deeper, and more useful understanding of a concept or process. Even though concept development and technology are emphasized, manipulative skills are not ignored, and plenty of opportunities to practice basic skills are present. A brief look at the table of contents will reveal the importance of the function concept as a unifying theme. The second major objective of this book is the development of a library of elementary functions, including their important properties and uses. Having this library of elementary functions as a basic working tool in their mathematical tool boxes, students will be able to move into calculus with greater confidence and understanding. In addition, a concise review of basic algebraic concepts is included in Appendix A for easy reference, or systematic review. The third major objective of this book is to give the student substantial experience in solving and modeling real world problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful. Most of the applications are simplified versions of actual real-world problems taken from professional journals and professional books. No specialized experience is required to solve any of the applications.
From the Publisher
Examples and Matched Problems:
Integrated throughout the text, completely worked examples and practice problems are used to introduce concepts and demonstrate problem-solving techniques. Each example is followed by a similar matched problem for the student to work through while reading the material. Answers to the matched problems are located at the end of each section, for easy reference. This active involvement in the learning process helps students develop a more thorough understanding of algebraic concepts and processes.
Exploration and Discussion:
Interspersed at appropriate places in every section, Explore-Discuss boxes present open-ended questions for exploration and lively discussion. The questions posed in these boxes encourage students to think critically about mathematics and are excellent opportunities for additional group work. Verbalization of mathematical concepts, results, and processes is encouraged in these Explore-Discuss boxes, as well as in some matched problems, and in particular problems in almost every exercise set. Explore-Discuss material can be used in class, or as an out-of-class activity.
Balanced Exercise Sets:
Precalculus: A Graphing Approach contains over 5,600 problems. Each exercise set is designed so that an average or below-average student will experience success and a
very capable student will be challenged. Exercise sets are found at the end of each section in the text, and are divided into A (routine, easy mechanics), B (more difficult mechanics), and C (difficult mechanics and some theory) levels of difficulty so that students at all levels can be challenged. Writing exercises are included in most sections and are clearly marked with a writing icon.
Applications:
One of the primary objectives of this book is to give the student substantial experience in modeling and solving real-world problems. Over 700 application exercises help convince even the most skeptical student that mathematics is relevant to every day life. The
most difficult application problems are marked with two stars ( ), the
moderately difficult application problems with one star (-), and the
easier application problems are not marked. An Applications Index is included to help locate particular applications.
Group Activities:
A Group Activity is located at the end of each chapter and involves many of the concepts discussed in that chapter. These activities strongly encourage the verbalization of mathematical concepts, results, and processes. All of these special activities are highlighted to emphasize their importance.
Technology:
The generic term 'graphing utility' is used to refer to any of the various graphing calculators or computer software packages that might be available to a student using this book. The use of technology is integrated throughout the text for visualization, investigation, and verification.
Chapter Opener:
Each chapter opens with a real-world application. Complete solutions to the chapter opener applications are located at the end of each chapter review, and require the use of graphical, numerical, and algebraic problem solving techniques.
Graphs and Illustrations:
All graphs in this text are computer generated to ensure mathematical accuracy. Graphing utility screens displayed in the text are actual output from a graphing calculator.
Foundation for Calculus:
As many students will use this book to prepare for a calculus course, examples and exercises that are especially pertinent to a student's future study of calculus are marked with a special icon.
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