Precalculus: An Investigation of Functions (Includes Trig)

David Lippman, Melonie Rasmussen

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.

This book is also available as a split volume, with the first being the narrative text, and the second being the problem sets.

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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 Rational Functions
    • 3.5 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 Parametric Equations
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