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.

# 17 Results

This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.

- Subject:
- Functions
- Material Type:
- Textbook
- Provider:
- Virginia Commonwealth University
- Author:
- Richard Hammack
- Date Added:
- 01/01/2009

This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

- Subject:
- Health, Medicine and Nursing
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Lesson Plan
- Provider:
- National Association of State Directors of Career Technical Education Consortium
- Provider Set:
- Career Technical Education
- Date Added:
- 07/27/2012

This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

- Subject:
- Health, Medicine and Nursing
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Lesson Plan
- Provider:
- National Association of State Directors of Career Technical Education Consortium
- Provider Set:
- Career Technical Education
- Date Added:
- 07/26/2012

This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)

- Subject:
- Calculus
- Functions
- Material Type:
- Assessment
- Full Course
- Reading
- Syllabus
- Textbook
- Provider:
- The Saylor Foundation
- Date Added:
- 04/16/2012

This course is an introduction to contemporary calculus and is the first of a three-part sequence. In this course students explore the concepts, applications, and techniques of Calculus - the mathematics of change. Calculus has wide-spread application in science, economics and engineering, and is a foundation college course for further work in these areas. This is a required class for most science and mathematics majors.Login: guest_oclPassword: ocl

- Subject:
- Calculus
- Functions
- Material Type:
- Full Course
- Homework/Assignment
- Lecture Notes
- Lesson Plan
- Reading
- Syllabus
- Provider:
- Washington State Board for Community & Technical Colleges
- Provider Set:
- Open Course Library
- Date Added:
- 10/31/2011

We told you about the derivatives of many functions, but you might want proof that what we told you is actually true. That's what this tutorial tries to do!

- Subject:
- Calculus
- Functions
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Date Added:
- 05/30/2013

This lab is an investigation into exponential and logarithmic functions. The lab helps students understand the visual graph of exponential functions and logarithmic functions. It also shows how transformations are shown on a graph as well as the connection between logarithmic and exponential functions. The lab uses desmos.com and takes 30-45 minutes.

- Subject:
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Author:
- Dr. Mary Alice Smeal
- Date Added:
- 06/03/2019

This lab is an investigative lab to help students make a visual connection between quadratic and polynomial functions and their graphs. The lab uses desmos.com and takes about 30-45 minutes.

- Subject:
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Author:
- Dr. Mary Alice Smeal
- Date Added:
- 06/03/2019

KiteModeler was developed in an effort to foster hands-on, inquiry-based learning in science and math. KiteModeler is a simulator that models the design, trimming, and flight of a kite. The program works in three modes: Design Mode, Trim Mode, or Flight Mode. In the Design Mode (shown below), you pick from five basic types of kite designs. You can then change design variables including the length and width of various sections of the kite. You can also select different materials for each component. When you have a design that you like, you switch to the Trim Mode where you set the length of the bridle string and tail and the location of the knot attaching the bridle to the control line. Based on your inputs, the program computes the center of gravity and pressure, the magnitude of the aerodynamic forces and the weight, and determines the stability of your kite. With a stable kite design, you are ready for Flight Mode. In Flight Mode you set the wind speed and the length of control line. The program then computes the sag of the line caused by the weight of the string and the height and distance that your kite would fly. Using all three modes, you can investigate how a kite flies, and the factors that affect its performance.

- Subject:
- Algebra
- Calculus
- Functions
- Trigonometry
- Material Type:
- Simulation
- Provider:
- NASA
- Provider Set:
- NASA Glenn Research Center
- Date Added:
- 02/16/2011

This lab investigates the transformations vertically and horizontally of basic functions graphs like square root, absolute value, and quadratics. The lab uses desmos.com and is very user friendly. The lab takes about 30 - 45 minutes.

- Subject:
- Algebra
- Functions
- Material Type:
- Activity/Lab
- Author:
- Dr. Mary Alice Smeal
- Date Added:
- 06/04/2019

This shows how Newton's method (also known as Newton-Raphson) is used to find a root of a function. You can show/hide various parts of the construction, and edit the particular function being considered.

- Subject:
- Functions
- Geometry
- Material Type:
- Simulation
- Provider:
- GeoGebra
- Provider Set:
- GeoGebraTube
- Date Added:
- 03/12/2012

Based on the College and Career Readiness Standards in Action- 25% of higher level math instruction should be spent on Algebra and Functions. This includes Interpreting quadratic equations, using their structure to rewrite them in equivalent forms which serve a purpose. Also creating and solving quadratic equations to solve problems, both algebraically and graphically. They are to be able to re-arrange formulas involving quadratics and highligh specific quantities. (Guide to Effectively Managing Higher-Level Content Standards in Mathematics.)The amount of OER material available to assist instruction in higher level EFL math for adults is numerous, but searching for it often gets one tangled in the pedigogical instruction, with simplistic "real-life" examples, whereas adults with REAL "real-life" experience can appreciate the topics applied to broader world examples. This curriculum guide will give suggestions for pre-lesson activities to stimulate prior knowledge, walk you through a lesson example, and hopefully whet your appetite for using OER's in your regular instruction.

- Subject:
- Applied Science
- Algebra
- Functions
- Measurement and Data
- Material Type:
- Module
- Author:
- Lori Lundine
- Date Added:
- 05/08/2018

The material was written with review in mind, but there is enough detail that it would be useful for new students as well. Each topic includes written introductions, detailed examples, and practice exercises that are fully keyed. In addition, each chapter concludes with additional practice problems – those problems are not keyed, although short answers are provided. Many topics also include videos.

- Subject:
- Mathematics
- Algebra
- Functions
- Numbers and Operations
- Material Type:
- Assessment
- Interactive
- Author:
- Steve Simonds
- Date Added:
- 09/25/2018

This OER course using a new textbook is based a section of MAT103 Pre-Calculus. It is a preparatory course for Calculus. It builds upon the intermediate level of Algebra and makes intensive use of technology to conceptualize functions and methods of function manipulation with emphasis on quantitative change. All course content written by Fahmil Shah. Added to OER Commons by Victoria Vidal.

- Subject:
- Algebra
- Calculus
- Functions
- Trigonometry
- Material Type:
- Full Course
- Provider:
- Roxbury Community College
- Author:
- Fahmil Shah
- Date Added:
- 05/10/2022

This course will cover families of functions, their properties, graphs and applications. These functions include: polynomial, rational, exponential, logarithmic functions and combinations of these. We will solve related equations and inequalities and conduct data analysis, introductory mathematical modeling and develop competency with a graphing calculator.Login: guest_oclPassword: ocl

- Subject:
- Functions
- Material Type:
- Full Course
- Homework/Assignment
- Lecture Notes
- Lesson Plan
- Reading
- Syllabus
- Provider:
- Washington State Board for Community & Technical Colleges
- Provider Set:
- Open Course Library
- Date Added:
- 10/31/2011

This lesson covers the topic of Time Value of Money and prepares students for lessons on simple interest loans (operating notes and lines of credit) and amortized loans. It introduces the ideas of present and future values, compounding and discounting, payements and time periods. It uses Microsoft Excel extensively as an aid for problem calculations.

- Subject:
- Finance
- Agriculture
- Functions
- Material Type:
- Activity/Lab
- Primary Source
- Author:
- Tyler Schau
- Date Added:
- 05/11/2020