
Precalculus 2e
by Jay Abramson
Published by OpenStax
Precalculus 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical precalculus course. The text proceeds from functions through trigonometry and ends with an introduction to calculus. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Precalculus 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned. The Precalculus 2e revision focused on improving relevance and representation as well as mathematical clarity and accuracy. Introductory narratives, examples, and problems were reviewed and revised using a diversity, equity, and inclusion framework. Many contexts, scenarios, and images have been changed to become even more relevant to students’ lives and interests. To maintain our commitment to accuracy and precision, examples, exercises, and solutions were reviewed by multiple faculty experts. All improvement suggestions and errata updates from the first edition were considered and unified across the different formats of the text. The first edition of Precalculus by OpenStax is available in web view here . If you have encountered a white screen while accessing your OpenStax textbook, our developers suggest closing all of your OpenStax.org tabs and then loading the book again.
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Attribution
Adapted from Precalculus 2e by Jay Abramson, published by OpenStax (Rice University) under CC BY-NC-SA 4.0 (https://creativecommons.org/licenses/by-nc-sa/4.0/). Access the original for free at https://openstax.org/details/books/precalculus-2e. Changes: converted to CuraCourse lessons, with interactive practice added.
Table of contents
99 pages in 14 modules. Sign up to read and adopt them.
Preface1 page
- Preface
1Functions9 pages
- Introduction to Functions
- 1.1Functions and Function Notation
- 1.2Domain and Range
- 1.3Rates of Change and Behavior of Graphs
- 1.4Composition of Functions
- 1.5Transformation of Functions
- 1.6Absolute Value Functions
- 1.7Inverse Functions
- Practice
2Linear Functions6 pages
- Introduction to Linear Functions
- 2.1Linear Functions
- 2.2Graphs of Linear Functions
- 2.3Modeling with Linear Functions
- 2.4Fitting Linear Models to Data
- Practice
3Polynomial and Rational Functions11 pages
- Introduction to Polynomial and Rational Functions
- 3.1Complex Numbers
- 3.2Quadratic Functions
- 3.3Power Functions and Polynomial Functions
- 3.4Graphs of Polynomial Functions
- 3.5Dividing Polynomials
- 3.6Zeros of Polynomial Functions
- 3.7Rational Functions
- 3.8Inverses and Radical Functions
- 3.9Modeling Using Variation
- Practice
4Exponential and Logarithmic Functions10 pages
- Introduction to Exponential and Logarithmic Functions
- 4.1Exponential Functions
- 4.2Graphs of Exponential Functions
- 4.3Logarithmic Functions
- 4.4Graphs of Logarithmic Functions
- 4.5Logarithmic Properties
- 4.6Exponential and Logarithmic Equations
- 4.7Exponential and Logarithmic Models
- 4.8Fitting Exponential Models to Data
- Practice
5Trigonometric Functions6 pages
- Introduction to Trigonometric Functions
- 5.1Angles
- 5.2Unit Circle: Sine and Cosine Functions
- 5.3The Other Trigonometric Functions
- 5.4Right Triangle Trigonometry
- Practice
6Periodic Functions5 pages
- Introduction to Periodic Functions
- 6.1Graphs of the Sine and Cosine Functions
- 6.2Graphs of the Other Trigonometric Functions
- 6.3Inverse Trigonometric Functions
- Practice
7Trigonometric Identities and Equations8 pages
- Introduction to Trigonometric Identities and Equations
- 7.1Simplifying and Verifying Trigonometric Identities
- 7.2Sum and Difference Identities
- 7.3Double-Angle, Half-Angle, and Reduction Formulas
- 7.4Sum-to-Product and Product-to-Sum Formulas
- 7.5Solving Trigonometric Equations
- 7.6Modeling with Trigonometric Functions
- Practice
8Further Applications of Trigonometry10 pages
- Introduction to Further Applications of Trigonometry
- 8.1Non-right Triangles: Law of Sines
- 8.2Non-right Triangles: Law of Cosines
- 8.3Polar Coordinates
- 8.4Polar Coordinates: Graphs
- 8.5Polar Form of Complex Numbers
- 8.6Parametric Equations
- 8.7Parametric Equations: Graphs
- 8.8Vectors
- Practice
9Systems of Equations and Inequalities10 pages
- Introduction to Systems of Equations and Inequalities
- 9.1Systems of Linear Equations: Two Variables
- 9.2Systems of Linear Equations: Three Variables
- 9.3Systems of Nonlinear Equations and Inequalities: Two Variables
- 9.4Partial Fractions
- 9.5Matrices and Matrix Operations
- 9.6Solving Systems with Gaussian Elimination
- 9.7Solving Systems with Inverses
- 9.8Solving Systems with Cramer's Rule
- Practice
10Analytic Geometry7 pages
- Introduction to Analytic Geometry
- 10.1The Ellipse
- 10.2The Hyperbola
- 10.3The Parabola
- 10.4Rotation of Axes
- 10.5Conic Sections in Polar Coordinates
- Practice
11Sequences, Probability and Counting Theory9 pages
- Introduction to Sequences, Probability and Counting Theory
- 11.1Sequences and Their Notations
- 11.2Arithmetic Sequences
- 11.3Geometric Sequences
- 11.4Series and Their Notations
- 11.5Counting Principles
- 11.6Binomial Theorem
- 11.7Probability
- Practice
12Introduction to Calculus6 pages
- Introduction to Calculus
- 12.1Finding Limits: Numerical and Graphical Approaches
- 12.2Finding Limits: Properties of Limits
- 12.3Continuity
- 12.4Derivatives
- Practice
Appendices1 page
- ABasic Functions and Identities