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.

# 26 Results

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.

- Subject:
- Mathematics
- Calculus
- Material Type:
- Textbook
- Author:
- Matthew Boelkins
- Date Added:
- 02/18/2022

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

- Subject:
- Mathematics
- Material Type:
- Lesson
- Author:
- Igor Baryakhtar
- Date Added:
- 03/04/2021

This site has two PreCalculus Trigonometry textbooks and a PreCalculus Essentials textbook

- Subject:
- Mathematics
- Algebra
- Trigonometry
- Material Type:
- Textbook
- Author:
- Dewey Dellinger
- Date Added:
- 08/29/2022

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

- Subject:
- Mathematics
- Trigonometry
- Material Type:
- Teaching/Learning Strategy
- Author:
- Igor Baryakhtar
- Date Added:
- 07/19/2022

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

- Subject:
- Mathematics
- Material Type:
- Full Course
- Author:
- Khan Academy
- Date Added:
- 12/03/2020

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.

- Subject:
- Mathematics
- Material Type:
- Full Course
- Provider:
- U.C. Irvine
- Provider Set:
- UCI Open
- Author:
- Rachel Lehman
- Sarah Eichorn
- Date Added:
- 03/14/2018

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

- Subject:
- Business and Communication
- Mathematics
- Material Type:
- Activity/Lab
- Data Set
- Lecture Notes
- Provider:
- Science Education Resource Center (SERC) at Carleton College
- Provider Set:
- Starting Point (SERC)
- Author:
- Semra Kilic-Bahi
- Date Added:
- 08/28/2012

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.

- Subject:
- Mathematics
- Material Type:
- Full Course
- Author:
- Libby Gore
- Date Added:
- 05/31/2017

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.

- Subject:
- Calculus
- Material Type:
- Activity/Lab
- Homework/Assignment
- Provider:
- University System of Georgia
- Author:
- Marcela Chiorescu
- Rachel Epstein
- Date Added:
- 10/03/2022

Open source precalculus textbook.

- Subject:
- Calculus
- Material Type:
- Textbook
- Provider:
- Stitz-Zeager Open Source Mathematics
- Author:
- Carl Stitz
- Jeff Zeager
- Date Added:
- 07/15/2011

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.

- Subject:
- Calculus
- Material Type:
- Textbook
- Provider:
- A.T. Still University
- Author:
- David H. Collingwood
- K. David Prince
- Matthew M. Conroy
- Date Added:
- 12/03/2019

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.

- Subject:
- Mathematics
- Material Type:
- Textbook
- Provider:
- Rice University
- Provider Set:
- OpenStax College
- Author:
- David Lippman
- Jay Abramson
- Jean-Marie Magnier
- Melonie Rasmussen
- Nicholas Belloit
- Rachael Gross
- Rick Norwood
- Valeree Falduto
- Date Added:
- 02/20/2014

From the preface, "These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems."

- Subject:
- Calculus
- Material Type:
- Textbook
- Provider:
- CUNY Academic Works
- Provider Set:
- New York City College of Technology
- Author:
- Holly Carley
- Thomas Tradler
- Date Added:
- 09/01/2015

Precalculus 1 & 2 / Trigonometry provides a study of functions and their graphs, including polynomial, rational, exponential, and logarithmic functions. Additionally, right-triangle trigonometry, trigonometric functions and their applications are covered.

- Subject:
- Calculus
- Trigonometry
- Material Type:
- Full Course
- Textbook
- Provider:
- Lumen Learning
- Provider Set:
- Candela Courseware
- Author:
- David Lippman
- Melonie Rasmussen
- Date Added:
- 03/31/2016

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. 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.

Open Textbooks for Rural Arizona participants are invited to remix this template to share their courses, textbooks, and other OER material on our Hub.

- Subject:
- Education
- Mathematics
- Calculus
- Material Type:
- Textbook
- Author:
- Linda Neff
- Date Added:
- 11/30/2022

Module 2 extends the concept of matrices introduced in Module 1. Students look at incidence relationships in networks and encode information about them via high-dimensional matrices. Matrix properties are studied as well as the role of the zero and identity matrices. Students then use matrices to study and solve higher order systems of equations. Vectors are introduced, and students study the arithmetic of vectors and vector magnitude. The module ends as students program video games using matrices and vectors.

- Subject:
- Mathematics
- Material Type:
- Module
- Provider:
- New York State Education Department
- Provider Set:
- EngageNY
- Date Added:
- 03/24/2016

Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascals Triangle to find roots of polynomials and roots of unity. Students compare and create different representations of functions while studying function composition, graphing functions, and finding inverse functions.

- Subject:
- Mathematics
- Material Type:
- Module
- Provider:
- New York State Education Department
- Provider Set:
- EngageNY
- Date Added:
- 03/24/2016