HSC Together Year 11 Maths Advanced: Odd and Even Functions

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Odd and Even Functions

What are odd and even functions?

In this post, we define odd and even functions algebraically and recognise their geometric properties, as a part of the Prelim Maths Advanced course under the topic Working with Functions and sub-part Introduction to Functions. An odd function is a function with rotational symmetry of two, meaning if rotated 180^{o} it will be the exact same graph. An even function is symmetrical along the y-axis, meaning if it was folded along the y-axis, each side would match one another.

Introduction to odd and even functions

The following two videos introduce the geometric and algebraic definitions and properties of odd and even functions. The first video goes in-depth about examples, while the second covers the algebraic formulas used to prove odd and even functions.

Part 1

 

Part 2

 

Examples of odd and even functions

This video gives a large amount of worked examples of odd, even, and neither functions that can be used to solidify your understanding of odd and even functions.

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