Texas Instruments
Texas Instruments: Video Tutorial Learn How to Evaluate Composite Functions
In this video, you will see how to evaluate composite functions both numerically on the home screen and through the graph screen.
Other
Brilliant: Function Composition
Discusses the topic of function composition. Includes multiple examples and a quiz related to this topic.
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.
Oswego City School District
Regents Exam Prep Center: Composition of Functions
Defines and discusses composition of functions and what happens to the individual elements throughout the composition. Includes two worked examples.
Purple Math
Purplemath: Composition of Functions: Composing Functions With Functions
Explanations and examples of composing functions with functions.
Math Is Fun
Math Is Fun: Composition of Functions
A reference sheet with detailed explanations, examples, and practice problems for function composition.
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.
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.
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.
Lumen Learning
Lumen: Boundless Algebra: Inverse and Composite Functions
The resource discusses the topic of function composition. Includes multiple examples and a quiz on this topic.
Cool Math
Coolmath: Advanced Composition of Functions
A precalculus tutorial on the advanced composition of functions.
Illustrative Mathematics
Illustrative Mathematics: F Bf,if the Canoe Trip, Variation 1
In this task about canoeing, learners must analyze paddling speed and current speed, which are working against each other, to determine how long a canoe trip would take. They write expressions and analyze characteristics of the graph...
Illustrative Mathematics
Illustrative Mathematics: F Bf Building Explicit Quadratic Function: Composition
For this task, students work through the steps and operations involved in the composition of an explicit quadratic function. The task assumes that the students are familiar with the process of completing the square. Aligns with F-BF.B.3...
Illustrative Mathematics
Illustrative Mathematics: F Bf Temperature Conversions
In this task involving temperature conversions, young scholars compose and solve functions. Unit conversion problems provide a rich source of examples for the composition of functions and for inverses. Aligns with F-BF.A.1.c and F-BF.B.4.a.
Illustrative Mathematics
Illustrative Mathematics: F Bf Flu on Campus
In this task, students analyze data about the number of students being infected during an influenza outbreak. The purpose of this problem is to have students compose functions using tables of values only. Aligns with F-BF.A.1.c.
Illustrative Mathematics
Illustrative Mathematics: F Bf Graphs of Compositions
This task addresses an important issue about inverse functions. In this case, the function f is the inverse of the function g but g is not the inverse of f unless the domain of f is restricted. Aligns with F-BF.A.1.c.
Illustrative Mathematics
Illustrative Mathematics: F Bf Crude Oil and Gas Mileage
For this task, students write expressions that describe the relationship between quantities. The task looks at the amount of gas produced by a given number of barrels of crude oil, the number of miles a vehicle can drive on a quantity of...
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.
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.
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.
CK-12 Foundation
Ck 12: Composition of Inverse Reciprocal Trig Functions
[Free Registration/Login may be required to access all resource tools.] On this site students learn about the composition of inverse trigonometric functions. Students read about inverse reciprocal functions, watch a video about the topic...
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...
CK-12 Foundation
Ck 12: Analysis: Composition of Functions
[Free Registration/Login may be required to access all resource tools.] This lesson provides an introduction to the composition or combination of functions.
Help Algebra
Help algebra.com: How to Find Compositions of Functions
Learn how to notate and evaluate composite functions with this article. The examples are detailed and provide steps for finding the composition of two functions.