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

• 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.

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

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.