This week we will examine the concept of a function, a fundamental concept underlying all of modern mathematics. You’re undoubtedly already familiar with functions in an intuitive sense: a function is something which, given
an input, produces an output. But you’ve probably never seen the formal definition of a function as it relates to set theory, which is what we’ll look at this week.

This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.

This text is designed for college students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes how it is important in calculus.

This is the FlexBook 2.0 version of CK-12's PreCalculus Concepts course. In addition to new formatting and access to teacher insights, there are many curated 'Related Modalities' for each lesson. The text surveys traditional and additional content for a course in sequence after Algebra II and before Calculus or Statistics. The content in this text covers most state standards for Analysis, Trigonometry and Linear Algebra as well as the Common Core Standards suggested for a "Fourth Course" in high school.

This posting explains the concept of a function, the notation, domain and range of a function, and the basic ways to define a function.

The Exponents and Radicals module is separated into two parts -- exponents and radicals.  Each part has two subtopics. Each subtopic has a video lecture page and a practice assignment. The video lecture page includes guided notes in pdf form and videos that follow the guided notes.  There are also Word document versions of the notes in the "files" section of this course for instructor convenience.  Each video lecture page also includes supplemental YouTube videos which are optional for students and may be used if further instruction is needed.  The practice assignment is a set of exercises in Derivita that correspond to the skills covered in the video lecture.There are also two review assignments in this module -- one for exponents and one for radicals.  These assignments cover everything from that part of the module, rather than being broken up into parts like the practice assignments. So there are a total of six assignments in the module and instructors can choose which assignments are most appropriate for their students' needs.This work, by Madilyn Marshall, is licensed under a Creative Commons Attribution 4.0 International License.CC-BY

The Factoring module is separated into two parts -- factoring numbers and factoring algebraic expressions.  Each part has subtopics. Each subtopic has a video lecture and a practice assignment.  The video lecture page includes guided notes in pdf form and videos that follow the guided notes.  Each video lecture page also includes supplemental YouTube videos which are optional for students and may be used if further instruction is needed.  The practice assignment is a set of exercises in Derivita that correspond to the skills covered in the video lecture.This work, by Magdalene (Maxie) Inigo, is licensed under a Creative Commons Attribution 4.0 International License.Links to an external site.CC-BY

The Fraction module is separated into five pages.  Each page except the first page has videos and lecture notes. At the end of the entire module are review problems. The review problems are a set of exercises in Derivita that correspond to the skills covered in the lecture pages and the videos.The instructors can choose to assign the practice problems based on their students' needs.This work was created by Kathryn Kozak, and it is licensed under a Creative Commons Attribution 4.0 International License.CC-BY

Presentation Slides for 17th Annual Massachusetts Colleges Online  Conference on eLearning, June 2nd, 2022.

This course covers Complex Number, Polynomials, Composite Functions, Trigonometry, Vectors, Matrices, Series, Conic Sections, and Probability and combinatorics.

Precalculus Course with newly added video content in Spanish in weeks 01 and 02, more to come.

This Pre-Calculus course is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus.

In this activity, we will explore how the dosage and frequency of a medicine taken affect the amount of medicine present in the blood.

This resource is a collection of full hour-long lectures and accompanying notes covering most of chapters 6-10 of the OpenStax Algebra and Trigonometry book. The notes are provided in both .DOCX and .PDF format to accommodate downloading ease. Students should be encouraged to print notes and fill them out as they watch through the lectures.

This collection of worksheets, homework assignments, and study skills exercises was created through a Round 14 Textbook Transformation Grant. The worksheets supplement the following topics as covered in OpenStax Precalculus: Functions, domain and range, rates of change, inverse functions, exponential functions, logarithmic functions, exponential growth modeling, angles, sine and cosine, right triangles, sum identities, and difference identities. Study skills exercises include growth mindset and metacognition activities.

This Pre-Calculus Review handbook supplements via ancillary notes and practice problems from the OER textbooks 1. Apex PreCalculus, 2. OpenStax Algebra & Trigonometry – 2nd edition
and 3. OpenStax PreCalculus – 2nd edition. The text allows for a greater synergy between the calculus and pre-calculus portions of the course.

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.

Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind:

A review of the essential mathematics needed to succeed in calculus.
An emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical tools.
This text was created to achieve these goals and the 2004-05 academic year marks the eleventh year in which it has been used. Several thousand students have successfully passed through the course.

This book is full of worked out examples. We use the the notation “Soluion.” to indicate where the reasoning for a problem begins; the symbol ?? is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the final examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with ”answers” to most of the problems in the text. It should be emphasized these are ”answers” as opposed to ”solutions”. Any homework problems you may be asked to turn in will require you include all your work; in other words, a detailed solution. Simply writing down the answer from the back of the text would never be sufficient; the answers are intended to be a guide to help insure you are on the right track.