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Precalculus: An Investigation of Functions (Includes Trig) 2nd Ed by David Lippman, Melonie Rasmussen

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The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.

The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisited more extensively in the third chapter. As with the first part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation.

This book attempts to find a balance between a modern approach to precalculus focusing on applications, problem solving, and concepts and a traditional approach, emphasizing the basic skills needed for calculus.

The second edition adds sections on real and complex roots of polynomials, dot product, and a new chapter on conics.

License: Creative Commons Attribution Sharealike. This license is considered to be some to be the most open license. It allows reuse, remixing, and distribution (including commercial), but requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license.
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  • Chapter 1: Functions
    • 1.1: Functions and Function Notation
    • 1.2 Domain and Range
    • 1.3 Rates of Change and Behavior of Graphs
    • 1.4 Composition of Functions
    • 1.5 Transformation of Functions
    • 1.6 Inverse Functions
  • Chapter 2: Linear Function
    • 2.1 Linear Functions
    • 2.2 Graphs of Linear Functions
    • 2.3 Modeling with Linear Functions
    • 2.4 Fitting Linear Models to Data
    • 2.5 Absolute Value Functions
  • Chapter 3: Polynomial and Rational Functions
    • 3.1 Power Functions & Polynomial Functions
    • 3.2 Quadratic Functions
    • 3.3 Graphs of Polynomial Functions
    • 3.4 Factor and Remainder Theorem
    • 3.5 Real Zeros of Polynomials
    • 3.6 Complex Zeros
    • 3.7 Rational Functions
    • 3.8 Inverses and Radical Functions
  • Chapter 4: Exponential and Logarithmic Functions
    • 4.1 Exponential Functions
    • 4.2 Graphs of Exponential Functions
    • 4.3 Logarithmic Functions
    • 4.4 Logarithmic Properties
    • 4.5 Graphs of Logarithmic Functions
    • 4.6 Exponential and Logarithmic Models
    • 4.7 Fitting Exponentials to Data
  • Chapter 5: Trigonometric Functions of Angles
    • 5.1 Circles
    • 5.2 Angles
    • 5.3 Points on Circles using Sine and Cosine
    • 5.4 The Other Trigonometric Functions
    • 5.5 Right Triangle Trigonometry
  • Chapter 6: Periodic Functions
    • 6.1 Sinusoidal Graphs
    • 6.2 Graphs of the Other Trig Functions
    • 6.3 Inverse Trig Functions
    • 6.4 Solving Trig Equations
    • 6.5 Modeling with Trigonometric Equations
  • Chapter 7: Trigonometric Equations and Identities
    • 7.1 Solving Trigonometric Equations with Identities
    • 7.2 Addition and Subtraction Identities
    • 7.3 Double Angle Identities
    • 7.4 Modeling Changing Amplitude and Midline
  • Chapter 8: Further Applications of Trigonometry
    • 8.1 Non-right Triangles: Law of Sines and Cosines
    • 8.2 Polar Coordinates
    • 8.3 Polar Form of Complex Numbers
    • 8.4 Vectors
    • 8.5 Dot Product
    • 8.6 Parametric Equations
  • Chapter 9: Conics
    • 9.1 Ellipses
    • 9.2 Hyperbolas
    • 9.3 Parabols and Non-Linear Systems
    • 9.4 Conics in Polar Coordinates

Supplements:

  • MyOpenMath / Lumen OHM online homework. MyOpenMath is a free online homework system, built on the open source IMathAS assessment platform. It provides randomized, algorithmically generated homework with automated grading of numerical and algebraic answers, similar to WebAssign and MyMathLab. It also provides a course management system with gradebook, file posting, discussion forums, etc. Assessment sets have been created for this textbook, which may be available for self-study by students, or can copied as a starter course shell by faculty.MyOpenMath use is free with community support through forums. For Washington State faculty, the WAMAP.org site also mirrors this content.

    Lumen OHM is a commercial alternative to MyOpenMath that provides support for faculty and large scale adoption and administration, service level agreements, and additional curated course bundles.

  • Videos. See the comments below for details.
  • CourseWare package. Courseware packages typically include a course structure with syllabus, some form of homework assignments, and some type of assessments. They may also include: videos, lecture notes, handouts, worksheets, quizzes, etc.
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