Education Technology

Dynagraphs

Published on 12/01/2011

Activity Overview

This lesson involves using a dynagraph to explore the relationship between the input and the output of a given function.

Objectives

  • Students will utilize the input and output of a function to determine its rule.
  • Students will discover conditions that would restrict a function's domain.
  • Students will understand that a composition utilizes the output of the inside function as the input of the outside function.
  • Students will understand the special relationship between two inverse functions and their composition.

Vocabulary

  • composite functions
  • composition
  • domain
  • inverse
  • range
  • restricted domain

About the Lesson

This lesson involves using a dynagraph to explore the relationship between the input and the output of a given function.
As a result, students will:

  • Discover how a composition utilizes the output of the inside function as the input of the outside function.
  • Determine the rule for a function, as well as the domain and range of the function.
  • Make and test predictions about the rule for two functions and for their composition.
  • Discover the special relationship between two inverse functions and their composition.