Functions and Graphs

by I. M. Gelfand, E. G. Glagoleva, E. E. Shnol

Overview

The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple functions to analyze the fundamental methods of constructing graphs. The second half deals with more complicated and refined questions concerning linear functions, quadratic trinomials, linear fractional functions, power functions, and rational functions.

Product Details

ISBN-13:	9780486317137
Publisher:	Dover Publications
Publication date:	03/12/2013
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	112
File size:	8 MB

Table of Contents

Foreword
Introduction
CHAPTER 1
Examples
CHAPTER 2
The Linear Function
CHAPTER 3
The Function y = x
CHAPTER 4
The Quadratic Trinomial
CHAPTER 5
The Linear Fractional Function
CHAPTER 6
Power Functions
CHAPTER 7
Rational Functions
Problems for Independent Solution
Answers and Hints to Problems and Exercises
Marked by the Sign

Editorial Reviews

"All through both volumes [Functions & Graphs and The Methods of Coordinates], one finds a careful description of the step-by-step thinking process that leads up to the correct definition of a concept or to an argument that clinches in the proof of a theorem. We are ... very fortunate that an account of this caliber has finally made it to printed pages... Anyone who has taken this guided tour will never be intimidated by n ever again... High school students (or teachers) reading through these two books would learn an enormous amount of good mathematics. More importantly, they would also get a glimpse of how mathematics is done."

— H. Wu, The Mathematical Intelligencer

From the Publisher