Functions and Graphs (Dover Books on Mathematics)

Rating:
Summary: A clear and simple look at functions and graphs
Review: Great book to help you remember how to do graphs. It has many pictures to keep you in track with what you are doing. It also has many examples and problems to illustrate the material.

Rating:
Summary: A great book!
Review: I tend to look at elementary books like this one from the point of someone who doesn't need to learn from it but might want to use it as a text if teaching or tutoring someone. I learned almost nothing from this book, but I didn't expect to, as it's all material I learned ages ago. But for someone encountering this material for the first time, this would be an excellent book.

I see this book as used primarily in a pre-calculus math class or for tutoring someone about to take calculus. It gives a good exposition of material that will be encountered at the time a student takes calculus, but at a level that assumes the student has only the algebra that most students entering a calculus course have taken. And from that point, it explains the elements of drawing graphs of algebraic functions and the ideas of tangency that are so critical to differential calculus, and does so in a clear way, with helpful diagrams. It is a slim book, and probably by itself could not be the only text in a pre-calculus math class, but on the subjects it covers, it is the best I have seen. (And that is underrating it, because there aren't many books on the subject. So one might say that "the best there is" isn't really as high praise as it deserves.)

This book certainly deserves a 5-star rating.

Rating:
Summary: An insightful introduction to analytic geometry.
Review: This brief text provides a clear introduction to analytic geometry. Its scope is narrow. The authors discuss the graphs and properties of linear functions, absolute value functions, quadratic functions, linear fractional functions, power functions, and rational functions (trigonometric functions are discussed in another volume of the Gelfand School Outreach Program). What distinguishes this book from other treatments of the same topics is the extent to which the authors go to explain, using both words and diagrams, why the graphs of the functions they discuss have the form they do and the many challenging exercises they include.

This book concludes with a chapter length exercise set full of challenging problems. The reader who completes these problems will gain a much fuller understanding of analytic geometry than one who reads a typical precalculus text. While calculus is not required to complete the exercises, the reader may wish to revisit these problems once she or he has had calculus in order to analyze the properties of the graphs more fully.

The text was written initially for a correspondence course in the Soviet Union. Since students could send their solutions to the authors when they were at the University of Moscow, answers or hints to only a few of the exercises are included in the back of the text.

I also highly recommend the other volumes in the Gelfand School Outreach Program. They include The Method of Coordinates, Algebra, and Trigonometry.