Functions and Graphs

CHAPTER 2 The Linear Function ( v : x of Jor = 45 ° Let us now begin to study systematically the behavior of different functions and to construct their graphs . The characteristic behavior of functions and peculiarities of their graphs ...

Author: I.M. Gelfand

Publisher: Springer Science & Business Media

ISBN: 0817635327

Category: Mathematics

Page: 106

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The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990's. As early as the 1960's, I.M. Gelfand and his colleagues in the USSR thought hard about this same question and developed a style for presenting basic mathematics in a clear and simple form that engaged the curiosity and intellectual interest of thousands of high school and college students. These same ideas, this same content, unchanged by over thirty years of experience and mathematical development, are available in the following books to any student who is willing to read, to be stimulated, and to learn. "Functions and Graphs" provides instruction in transferring formulas and data into geometrical form. Thus, drawing graphs is shown to be one way to "see" formulas and functions and to observe the ways in which they change. This skill is fundamental to the study of calculus and other mathematical topics. Teachers of mathematics will find here a fresh understanding of the subject and a valuable path to the training of students in mathematical concepts and skills.
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Zeta Functions of Graphs

There are also “non-Euclidean” graphs associated with finite fields, in which the distance is replaced by a finite ... Exercise 7.8 Consider the zeta function of the graph X obtained by removing one edge from the tetrahedron graph.

Author: Audrey Terras

Publisher: Cambridge University Press

ISBN: 9781139491785

Category: Mathematics

Page:

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Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.
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Functions and Graphs

Composite Functions and Inverse Functions MAA Problems 52 53 54 58 63 Chapter 5. Graphing Data from Equations Data from Functions Data from Sequences Graphs Define Functions Jargon Simultaneous Graphs MAA Problems 64 66 67 68 Chapter 6.

Author: James Tanton

Publisher: American Mathematical Soc.

ISBN: 9781470443498

Category: Education

Page: 218

View: 248

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A playful, readable, and thorough guide to precalculus, this book is directed at readers who would like a holistic look at the high school curriculum material on functions and their graphs. Tanton provides a coherent guided tour of exploration and discovery of a rich mathematical landscape. The exploration is presented through problems selected from the history of the Mathematical Association of America's American Mathematics Competition (AMC). Secondary school teachers looking for supplementary and enrichment materials will find this a rich resource, which aligns with national curriculum standards. High school and college calculus and precalculus students will discover an approachable and thought-provoking review, preview, and overview of these central mathematical ideas. Students preparing for the AMC should find it especially helpful. Active reading, with pencil in hand, will result in a deep appreciation and understanding of the properties of functions. James Tanton is the MAA's mathematician-at-large. A research mathematician with experience teaching at both the college and high school levels, he now works to encourage and aid all mathematics instructors to teach--and all mathematics students to learn--joyously and effectively.
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Precalculus Functions and Graphs

Functions are sometimes described by more than one expression, as in the next examples. We call such functions piecewise-defined functions. EXAMPLE 8 Sketching the graph of a piecewise-defined function Sketch the graph of the function ...

Author: Earl Swokowski

Publisher: Cengage Learning

ISBN: 9781133172512

Category: Mathematics

Page: 912

View: 431

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The latest edition of Swokowski and Cole's PRECALCULUS: FUNCTIONS AND GRAPHS retains the elements that have made it so popular with instructors and students alike: clear exposition, an appealing and uncluttered layout, and applications-rich exercise sets. The excellent, time-tested problems have been widely praised for their consistency and their appropriate level of difficulty for precalculus students. The book also provides calculator examples, including specific keystrokes that show students how to use various graphing calculators to solve problems more quickly. The Twelfth Edition features updated topical references and data, and continues to be supported by outstanding technology resources. Mathematically sound, this book effectively prepares students for further courses in mathematics. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
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Precalculus Functions and Graphs Enhanced Edition

10, 4 6, 15 112 2 Functions are sometimes described by more than one expression, as in the next examples. We call such functions piecewise-defined functions. Sketching the graph of a piecewise-defined function Sketch the graph of the ...

Author: Earl Swokowski

Publisher: Cengage Learning

ISBN: 9781305887954

Category: Mathematics

Page: 992

View: 217

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The Enhanced Edition of Swokowski and Cole’s PRECALCULUS: FUNCTIONS AND GRAPHS retains the elements in the Twelfth Edition that have made it so popular with instructors and students alike: clear exposition, an appealing and uncluttered layout, and applications-rich exercise sets. It features an additional chapter on Limits (Chapter 11) and an Appendix V that includes proofs related to this new chapter. The excellent, time-tested problems have been widely praised for their consistency and their appropriate level of difficulty for precalculus students. The book also provides calculator examples, including specific keystrokes that show students how to use various graphing calculators to solve problems more quickly. This Enhanced Edition features updated topical references and data and continues to be supported by outstanding technology resources. Mathematically sound, this book effectively prepares students for further courses in mathematics. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
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Functions and Graphs

This text demonstrates the fundamentals of graph theory.

Author: I. M. Gelfand

Publisher: Courier Corporation

ISBN: 9780486317137

Category: Mathematics

Page: 112

View: 781

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This text demonstrates the fundamentals of graph theory. The 1st part employs simple functions to analyze basics; 2nd half deals with linear functions, quadratic trinomials, linear fractional functions, power functions, rational functions. 1969 edition.
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Modeling Functions and Graphs

At this level, it is crucial that students learn to write an algebraic expression from a verbal description, to recognize trends in a table of data, and to extract and interpret information from the graph of a function. Graphs No tool ...

Author: Katherine Yoshiwara

Publisher: Cengage Learning

ISBN: 0534368328

Category: Algebra

Page: 901

View: 899

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Popular with and respected by students interested in a Modeling Approach, Graphing, or Graphing Calculators, this book incorporates the benefits of technology and the philosophy of the reform movement into intermediate algebra. In keeping with the NCTM and AMATYC standards, the authors introduce the techniques of algebra in the context of simple applications. Early and consistent emphasis on functions and graphing helps to develop mathematical models, and graphing calculators are incorporated wherever possible.
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Precalculus with Limits

2.2 Polynomial Functions of Higher Degree Use transformations to sketch graphs of polynomial functions. Use the Leading Coefficient Test to determine the end behaviors of graphs of polynomial functions. Find real zeros of polynomial ...

Author: Ron Larson

Publisher: Cengage Learning

ISBN: 9781337516853

Category: Mathematics

Page: 1120

View: 396

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Larson's PRECALCULUS WITH LIMITS is known for delivering the same sound, consistently structured explanations and exercises of mathematical concepts as the market-leading PRECALCULUS, with a laser focus on preparing students for calculus. In LIMITS, the author includes a brief algebra review of core precalculus topics along with coverage of analytic geometry in three dimensions and an introduction to concepts covered in calculus. With the Fourth Edition, Larson continues to revolutionize the way students learn material by incorporating more real-world applications, ongoing review, and innovative technology. How Do You See It? exercises give students practice applying the concepts, and new Summarize features, and Checkpoint problems reinforce understanding of the skill sets to help students better prepare for tests. The companion website LarsonPrecalculus.com offers free access to multiple tools and resources to supplement students’ learning. Stepped-out solution videos with instruction are available at CalcView.com for selected exercises throughout the text. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
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