Functions and operations

Functions are fundamental in mathematics, describing relationships between inputs and outputs.
For instance, linear functions are used to describe proportional relationships such as calculating cost based on price per unit. Quadratic functions are commonly used in physics to model projectile motion such as the trajectory of a ball. Exponential functions are widely used to represent population growth, radioactive decay and compound interest.
In addition, understanding the domain (possible inputs) and range (possible outputs) helps comprehend how functions behave and ensures the proper application of mathematical models. For instance, knowing the domain helps identify valid inputs – for example, time cannot be negative in certain contexts. Composite and combined functions introduce the concepts of function manipulation and how functions can be layered or combined to form new ones.
For instance, combining functions for atmospheric pressure and temperature leads to more accurate predictions of storm conditions. Piecewise functions dictate character behaviour in different zones, such as  walking on land versus swimming in water in gaming scenarios.

This resource revises functions and operations and within functions and operations there are 3 key concepts:

• Basics of Functions
• Composite functions
• Combined functions.

To determine if this resource will benefit you, start by answering the following questions.

• How are  the domain and range of a function determined, and why are certain values included or excluded?
• What is the difference between composite and inverse functions?
• When combining two functions, how do operations (addition, subtraction, multiplication or division) affect the results of the combined function’s behaviour?

The answers to these questions are provided on the following pages. Use this resource to refresh your memory, reinforce your understanding of these concepts, and prepare more effectively for university-level learning.

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