Curated OER
Blood Cell Basics
Students design a proportional model of blood out of red gelatin, a plastic bag, and rice. They study the components that make up blood and investigate what happens when the arteries in different scenerios. They work in pairs in order to...
Khan Academy
Khan Academy: Verifying Inverse Functions by Composition
Learn how to verify whether two functions are inverses by their composition. Students are given examples and practice problems.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Composition of Functions
A student asks Dr. Math how to evaluate a composite function. Dr. Math gives a systematic way to evaluate composite functions. Be sure to read the second response as well to findout how to evaluate functions of several compositions and...
Khan Academy
Khan Academy: Algebra Ii: Functions: Model With Composite Functions
Given two basic functions that model a real-world situation, compose them in order to model a more complex situation. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Find Composite Functions
Practice finding composite functions. The resource includes a video to support learning and students get instant feedback for their solutions.
Math Is Fun
Math Is Fun: Composition of Functions
A reference sheet with detailed explanations, examples, and practice problems for function composition.
Khan Academy
Khan Academy: Restrict Domains of Functions to Make Them Invertible
Given the graph of a function, find ways to restrict its domain in order to make it invertible. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Verify Inverse Functions
Given the formulas of two functions, compose the functions and determine whether they are inverses of each other. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
CK-12 Foundation
Ck 12: Algebra: Composition of Functions
[Free Registration/Login may be required to access all resource tools.] This lesson describes and demonstrates composition of functions. Students examine guided notes, review guided practice, watch instructional videos and attempt...
Khan Academy
Khan Academy: Determine if a Function Is Invertible
Given the table of values of a function, determine whether it is invertible or not by examining its domain. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Oswego City School District
Regents Exam Prep Center: Composition of Functions
This tutorial contains explanations and examples of functions that have been combined, or "compounded." The examples are easy to follow and are great for practice or review.
Analyze Math
Analyze Math: Tutorial on Compostion of Functions
This site offers a tutorial on compostion of functions. The tutorial works through several example problems to clarify the process.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Teaching Composition of Functions
Dr. Math gives several suggestions for teachers when helping students understand the concept of composition of functions.
Purple Math
Purplemath: Composition of Functions: Composing Functions With Functions
Explanations and examples of composing functions with functions.
Texas A&M University
Wtamu Virtual Math Lab: College Algebra: Operations With Functions
Learn how to perform operations with functions via viewing problems and step-by-step solutions and completing several practice problems and checking your work.
Interactive Mathematics
Interactive Mathematics: Functions and Graphs
The system created by Rene Descartes (1596-1650 CE) is explored in depth, covering topics such as definitions, notation, evaluating, domain and range, graphing and more. Interactive examples and demonstrations are enhanced using Live...
Mathematics Archives
Math Archives: Composition of Functions
Site offers a detailed explanation of the compostion of functions
Lawrence Hall of Science
The Math Page: An Approach to Calculus: The Chain Rule
Here is a site that clearly and thoroughly explains the chain rule for derivatives of composite functions. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point this site out...
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Composite Functions
Dr. Math explains a common mistake made by students with compostion of functions. Dr. Math goes through an example problem of function composition with a short explanation.
Wolfram Research
Wolfram Math World: Composition
A definition of composite functions and an investigation of their use in combinatorial compositions.
University of Saskatchewan (Canada)
University of Saskatchewan: Composition of Functions
This unique site allows one to enter two functions from a list of options, graphs both functions and their composition, then allows the user to trace any of the three via the java applet.
Math Medics
S.o.s. Math: The Chain Rule
Finding derivatives by using the chain rule is explained through examples in this tutorial.
University of California
Uc Davis: The Chain Rule
Nice comprehensive site on the chain rule the site explains the notation that goes along with the common notation of the chain rule through examples.