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. (See below for details of other books in this series.) 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. Unabridged republication of edition published by The M.I.T. Press, Cambridge, Massachusetts, 1969. Foreword. Introduction. Problems for Independent Solution.Gel'fand, I. M. is the author of 'Functions and Graphs' with ISBN 9780486425641 and ISBN 0486425649.