Mathematics & statistics
Precalculus: An Investigation of Functions
David Lippman, Melonie Rasmussen
OpenTextBookStore · Edition 2.3, July 2022 · English · Published 2022
A complete precalculus sequence covering functions, algebra, trigonometry and conics, with modeling examples and selected exercise answers.
- Learning stage
- High school
- Prerequisites
- High-school algebra and graph interpretation.
- PDF pages
- 704 in this file
- Editorial review
- 2026-10-29
Contents
Choose the section you need. Listening availability is shown for each section.
About the Authors
Acknowledgements
Preface
About the Second Edition
Instructor Resources
How To Be Successful In This Course
Table of Contents
Chapter 1: Functions
Chapter 1: Functions
Section 1.1 Functions and Function Notation
Section 1.1 Exercises
Section 1.2 Domain and Range
Section 1.2 Exercises
Section 1.3 Rates of Change and Behavior of Graphs
Section 1.3 Exercises
Section 1.4 Composition of Functions
Section 1.4 Exercises
Section 1.5 Transformation of Functions
Section 1.5 Exercises
Section 1.6 Inverse Functions
Section 1.6 Exercises
Chapter 2: Linear Functions
Chapter 2: Linear Functions
Section 2.1 Linear Functions
Section 2.1 Exercises
Section 2.2 Graphs of Linear Functions
Section 2.2 Exercises
Section 2.3 Modeling with Linear Functions
Section 2.3 Exercises
Section 2.4 Fitting Linear Models to Data
Section 2.4 Exercises
Section 2.5 Absolute Value Functions
Section 2.5 Exercises
Chapter 3: Polynomial and Rational Functions
Chapter 3: Polynomial and Rational Functions
Section 3.1 Power Functions & Polynomial Functions
Section 3.1 Exercises
Section 3.2 Quadratic Functions
Section 3.2 Exercises
Section 3.3 Graphs of Polynomial Functions
Section 3.3 Exercises
Section 3.4 Factor Theorem and Remainder Theorem
Section 3.4 Exercises
Section 3.5 Real Zeros of Polynomials
Section 3.5 Exercises
Section 3.6 Complex Zeros
Section 3.6 Exercises
Section 3.7 Rational Functions
Section 3.7 Exercises
Section 3.8 Inverses and Radical Functions
Section 3.8 Exercises
Chapter 4:
Exponential and Logarithmic Functions
Exponential and Logarithmic Functions
Section 4.1 Exponential Functions
Section 4.1 Exercises
Section 4.2 Graphs of Exponential Functions
Section 4.2 Exercises
Section 4.3 Logarithmic Functions
Section 4.3 Exercises
Section 4.4 Logarithmic Properties
Section 4.4 Exercises
Section 4.5 Graphs of Logarithmic Functions
Section 4.5 Exercises
Section 4.6 Exponential and Logarithmic Models
Section 4.6 Exercises
Section 4.7 Fitting Exponential Models to Data
Section 4.7 Exercises
Chapter 5: Trigonometric Functions of Angles
Chapter 5: Trigonometric Functions of Angles
Section 5.1 Circles
Section 5.1 Exercises
Section 5.2 Angles
Section 5.2 Exercises
Section 5.3 Points on Circles Using Sine and Cosine
Section 5.3 Exercises
Section 5.4 The Other Trigonometric Functions
Section 5.4 Exercises
Section 5.5 Right Triangle Trigonometry
Section 5.5 Exercises
Chapter 6:
Periodic Functions
Periodic Functions
Section 6.1 Sinusoidal Graphs
Section 6.1 Exercises
Section 6.2 Graphs of the Other Trig Functions
Section 6.2 Exercises
Section 6.3 Inverse Trig Functions
Section 6.3 Exercises
Section 6.4 Solving Trig Equations
Section 6.4 Exercises
Section 6.5 Modeling with Trigonometric Functions
Section 6.5 Exercises
Chapter 7: Trigonometric Equations and Identities
Chapter 7: Trigonometric Equations and Identities
Section 7.1 Solving Trigonometric Equations with Identities
Section 7.1 Exercises
Section 7.2 Addition and Subtraction Identities
Section 7.2 Exercises
Section 7.3 Double Angle Identities
Section 7.3 Exercises
Section 7.4 Modeling Changing Amplitude and Midline
Section 7.4 Exercises
Chapter 8: Further Applications of Trigonometry
Chapter 8: Further Applications of Trigonometry
Section 8.1 Non-Right Triangles: Laws of Sines and Cosines
Section 8.1 Exercises
Section 8.2 Polar Coordinates
Section 8.2 Exercises
Section 8.3 Polar Form of Complex Numbers
Section 8.3 Exercises
Section 8.4 Vectors
Section 8.4 Exercises
Section 8.5 Dot Product
Section 8.5 Exercises
Section 8.6 Parametric Equations
Section 8.6 Exercises
Chapter 9: Conics
Chapter 9: Conics
Section 9.1 Ellipses
Section 9.1 Exercises
Section 9.2 Hyperbolas
Section 9.2 Exercises
Section 9.3 Parabolas and Non-Linear Systems
Section 9.3 Exercises
Section 9.4 Conics in Polar Coordinates
Section 9.4 Exercises
Solutions to Selected Exercises
Solutions to Selected Exercises
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Index
Sources and permissions
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Author, publisher, and discovery sources
Authors: David Lippman, Melonie Rasmussen
Publisher: OpenTextBookStore
- Discovered through Open Textbook Library: Source record · Checked 2026-10-26
- Discovered through Open Textbook Library: Source record · Checked 2026-10-25
CC BY-SA 4.0
Precalculus: An Investigation of Functions, Edition 2.3, © 2022 David Lippman and Melonie Rasmussen. CC BY-SA 4.0. Original PDF unchanged; contributor, exercise and cover credits are retained. No endorsement implied.
Changes: Original PDF bytes are unchanged. Catalog metadata and page viewing are supplied by iReadAll. No endorsement implied. Structured extraction, audio, translation and independent image redistribution are not approved.
Checked 2026-10-29