Education Technology

### Mathematics lessons for IB® Diploma Programme

Analysis and Approaches | Functions

## Application of Function Composition

### Activity Overview

This lesson explores the composition of functions, their graphs and their application to real-world situations. As a result, students will:

• Interpret relationships between domain and range of two functions that produce a composite function.
• Analyze the data from a table that is generated from a model of a real-life situation that represents a composite function.
• Summarize the relationship between functions and their composite function.

### Objectives

• Given functions f and g, student will be able to determine the domain and range of each as well as the composite functions defined by f(g(x)) and g(f(x))
• Students will interpret the graphical relationship between two functions and their composition
• Students will determine relationships between two functions to create a composition of functions in the context of real-world applications

### Vocabulary

• Domain
• Range
• Composite functions