Math Tutorial 16.7 - Even and Odd Functions

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There are 10 lessons in this math tutorial covering Even and Odd Functions. The tutorial starts with an introduction to Even and Odd Functions and is then followed with a list of the separate lessons, the tutorial is designed to be read in order but you can skip to a specific lesson or return to recover a specific math lesson as required to build your math knowledge of Even and Odd Functions. you can access all the lessons from this tutorial below.

In this Math tutorial, you will learn:

What are even functions?
What is the condition for a function to be even?
How to check whether a function is even or not by substitution?
How to understand whether a function is even or not without substitutions?
What are the features of the graph of an even function?
What are the features of the graph of an odd function?
What happens if a function is neither even nor odd?
What are the properties of even functions?
What are the properties of odd functions?

Introduction

Consider the function f(x) = 2x². Pick two opposite values for x and substitute them in the function. What do you notice?

In the function g(x) = 4x³ - x pick one value for x. Now find f(-x) and -f(x). What do you notice?

Finally, do the above actions for the function h(x) = 3x² + 2x + 1. What do you notice?

In this tutorial, we will deal with even and odd functions - two types of functions that are very common and have many applications. Everything relating to odd and even functions, including the analysis, graph, properties, etc., will be explained and discussed in detail by illustrating the explanation with solved examples.

Please select a specific "Even and Odd Functions" lesson from the table below, review the video tutorial, print the revision notes or use the practice question to improve your knowledge of this math topic.

Functions Learning Material
Tutorial ID	Math Tutorial Title	Revision Notes	Revision Questions
16.7	Even and Odd Functions
Lesson ID	Math Lesson Title	Lesson	Video Lesson
16.7.1	Definition of Even Functions
16.7.2	How to Prove the Evenness of a Function Analytically
16.7.3	The Graph of Even Functions
16.7.4	Definition of Odd Functions
16.7.5	Proving the Oddness of a Function Analytically
16.7.6	The Graph of Odd Functions
16.7.7	Conclusions about the Evenness and Oddness of a Function
16.7.8	What If a Function is Neither Even Nor Odd?
16.7.9	Properties of Even Functions
16.7.10	Properties of Odd Functions

Whats next?

Enjoy the "Even and Odd Functions" math tutorial? People who liked the "Even and Odd Functions" tutorial found the following resources useful:

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Functions Revision Notes: Even and Odd Functions. Print the notes so you can revise the key points covered in the math tutorial for Even and Odd Functions
Functions Practice Questions: Even and Odd Functions. Test and improve your knowledge of Even and Odd Functions with example questins and answers
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Continuing learning functions - read our next math tutorial: Relation and Function

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