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: Algebra Ii: Graphs of Logarithmic Functions
Graph logarithmic functions and find the appropriate graph given the function. 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.
Analyze Math
Analyze Math: Derivative of Inverse Function
The tutorial explores the derivatives of inverse functions. Examples and practice exercises with solutions are included.
Analyze Math
Analyze Math: Domain and Range of Basic Functions
Learners examine a table of domain and range for basic functions. The tutorial includes the domain and range of algebraic, trigonometric, inverse trigonometric, hyperbolic, and logarithmic functions.
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...
Other
Karl's Calculus Tutor: Derivative of Inv. Trig Functions
This site provides a general overview of the derivative of inverse trig trunctions. Content includes a proof, exercises, and more.
Math Open Reference
Math Open Reference: Function
A complete reference guide to functions including how to use functions, inverse functions, graphing a function, and functions in computer programming. It provides definitions and examples that enhance further explanation.
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.
Khan Academy
Khan Academy: Graphs of Logarithmic Functions
Graph logarithmic functions and find the appropriate graph given the function.
CK-12 Foundation
Ck 12: 3.3 Inverse Functions
This section explores the process for finding inverses of functions, and then proving the function and its inverse algebraically. Additionally, it explores how the graphs of functions and their inverses compare to each other, and it...
Massachusetts Institute of Technology
Mit: Calculus Index
This site from the Massachussets Institute of Technology has links to various topics in calculus.
Wolfram Research
Wolfram Mathworld: Inverse Function
Site gives a definition of the inverse function as well as the example of the inverse of f(x)=x. Also included are formulas and links to related sites.
Wolfram Research
Wolfram Math World: One to One Functions
A site from Mathworld.com explaining One-to-One Functions. The site contains a definition and links to related sites.
Math Medics
S.o.s. Math: Exponential Functions
S.O.S. Math provides overviews, that include graphs, of the exponential function and the logarithmic function.
eFunda
Engineering Mathematics: Exponential and Logarithmic Functions
This site explains the Exponential and Logarithmic Functions and has links to plots of the functions.
Other
Gobierno De Navarra: Familias De Funciones Elementales
Visualize the different kinds of functions with these interactive activities.
Mathematics Archives
Math Archives: Visual Calculus: Odd Fuctions
Contains an example of an odd function.
Other
Radford Univ.: One to One Functions and Inverse Functions
This is a very short site from Radford University with a definition of One-To-One Functions and Inverse Functions.