Third, most of the initial exercises for each section are carefully coordinated with the worked examples in that section. With all the changes that come with this new edition, please rest assured that we have made every effort to maintain the quality and style that users of previous versions of the book have come to expect. We hope you will be pleased with this new edition. Also, for many college algebra students, there may be a gap of several years between their last mathematics course and the present one.
In Chapter 1, the reader is often referred to Appendix B for further practice. Graphs, visualization of data, and functions are now introduced much earlier and receive greater emphasis. Many sections contain examples and exercises involving applications and real-life data.
In addition to the Writing Mathematics sections from previous editions, there are Projects and Mini Projects. These, or references to them, appear at the ends of many sections. Writing Mathematics, Projects, and Mini Projects give students additional opportunities to discuss, explore, learn, and explain mathematics, often using real-life data.
We are also aware of the limitations of the graphing utility as a sole analysis device. The role of the graphing utility has continued to expand in this edition. The existence of the graphing utility is taken for granted, and a number of examples make use of this technology. However, just as in the previous edition, this remains a text in which the central focus is on mathematics and its applications.
If the instructor chooses, the text can be used without reference to the graphing utility, but a scientific calculator will be required for numerical calculations.
Students already familiar with a graphing utility will, at a minimum, need to read the explanation in Section 1. Graphing utility exercises identified by the symbol are integrated into the regular exercise sets. A complete presentation of trigonometry is given in Chapters 6— Some right-triangle material in Chapter 7, Section 5, is clearly labeled as being repeated from Chapter 6 and may be skipped.
To introduce trigonometry via the unit circle, merely skip Chapter 6, start with Chapter 7, and proceed through Chapter There are other major changes in this edition. Chapter 1. In Section 1. Symmetry to a point or to a line is based on pairs of points. We focus on the three basic symmetries of a curve: to the origin, to the x-axis, and to the y-axis.
From a pair of points with a particular symmetry we build to symmetry of a curve as a set of pairs of points with that symmetry. Next we discuss symmetry of a curve given by an equation. Then we focus on symmetry of the graph of a function. Throughout, we take advantage of two very useful facts. If a graph has any two of the three basic symmetries, then it must have all three basic symmetries.
In Section 2. Chapter 3. The material on graphing techniques in Section 3. In addition to vertical and horizontal shifts and reflections in the x-axis and y-axis, we cover vertical and horizontal scaling of graphs. Emphasis is on graphs of functions. There are two main types of problems. Given the equation of a graph that has been obtained by applying a sequence of transformations to the graph of a function, find the sequence of transformations.
In the latter situation, determining the sequence of transformations on the original graph, especially when unsure of a correct order, we find it useful to follow order of operation. Students can draw on their previous experience with order of operation and, perhaps more importantly, it always works! We break down transformations one at a time as listed in the Property Summary table on page The key idea is to determine how x or y changes at each step.
Finally, we conclude this section with an introduction to even functions and odd functions. In Section 3. We now start with the concept of a one-to-one function and then define an inverse function. The emphasis throughout is on the connection between a one-to-one function and its inverse function.
The theme is that any property of the inverse function is essentially a restatement of an already known property of the original function. In this way, domain and range, function values, and the graph of an inverse function follow immediately from corresponding information about the original function. Finally, using the fundamental relationships that the composition of a one-to-one function and its inverse function is an appropriate identity function, we can describe what an inverse function does and often find an explicit formula for the inverse function.
Chapter 4. Section 4. There is more detailed discussion and analysis of limiting behavior without using limits or limit notation. We start with a detailed analysis of the squaring and cubing functions. Using only algebra and symmetry, we determine increasing and decreasing behavior and end behavior for these power functions, including a careful comparison of the two. Tell me about Cengage eTextbooks. Best value! Access your book immediately!
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Download PDF Read online. Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer. Read online or offline instantly.
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