This is a mathematics textbook that covers mostly precalculus topics with some introductory calculus, as well as more advanced topics that are often not covered by a standard high school curriculum. A chapter proceeds by first establishing some central definitions and then further mathematical consequences, gradually developing the topic from scratch in the process. Unlike many other textbooks in precalculus, this book places emphasis on the art of mathematical proof, with an abundant supply of theorems, lemmas, and other problems that require such proofs. Detailed solutions and proofs are supplied as well.The main purpose is to aid readers who wish to learn precalculus and advanced supplemental topics through a more theoretical and abstract perspective and challenge their mathematical critical thinking skills rather than solve simple computational problems. The book is intended to develop the reader's conceptual understanding of the subject, as well as harness their curiosity in exploring such advanced topics. Furthermore, the book can be used as a supplementary text for students currently taking a precalculus or similar level math class who wish to learn more and go beyond the standard precalculus chapters, and into more abstract, advanced topics that are often not taught in many high schools at all.

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"Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of OpenStax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. OpenStax will also be releasing College Algebra and Algebra and trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses."--Preface.

Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives, and includes worked examples that demonstrate problem-solving approaches in an accessible way. Coverage and Scope Precalculus contains twelve chapters, roughly divided into three groups. Chapters 1-4 discuss various types of functions, providing a foundation for the remainder of the course. Chapter 1: Functions Chapter 2: Linear Functions Chapter 3: Polynomial and Rational Functions Chapter 4: Exponential and Logarithmic Functions Chapters 5-8 focus on Trigonometry. In Precalculus, we approach trigonometry by first introducing angles and the unit circle, as opposed to the right triangle approach more commonly used in College Algebra and Trigonometry courses. Chapter 5: Trigonometric Functions Chapter 6: Periodic Functions Chapter 7: Trigonometric Identities and Equations Chapter 8: Further Applications of Trigonometry Chapters 9-12 present some advanced Precalculus topics that build on topics introduced in chapters 1-8. Most Precalculus syllabi include some of the topics in these chapters, but few include all. Instructors can select material as needed from this group of chapters, since they are not cumulative. Chapter 9: Systems of Equations and Inequalities Chapter 10: Analytic Geometry Chapter 11: Sequences, Probability and Counting Theory Chapter 12: Introduction to Calculus