Table of Contents

## Introduction to Even and Odd Functions

A function is even if it produces the same result for every input when it is graphed on a coordinate plane. A function is odd if it produces a different result for every input when it is graphed on a coordinate plane. Even and Odd Functions – Explanation Properties Solved Examples and FAQs.

## Odd functions

An odd function is a function that is symmetrical about the y-axis. That is, if you reflect the function across the y-axis, the function will be the same. Odd functions are usually represented by the letter “f” followed by an “o” subscript.

## Even functions

Even functions are those functions that have an integer as their domain and range and that are symmetrical about the y-axis. That is, for every point (x, y) on the graph of an even function, there is another point (x, y) on the graph that is exactly the same distance from the y-axis, but on the opposite side of the y-axis.

## Some Basic Properties of Even Odd Functions

1. The even function is symmetric about the y-axis.

2. The even function is periodic with a period of 2π.

3. The even function is odd under a reflection in the y-axis.

4. The even function is anti-symmetric about the origin.

5. The even function is always positive.

## Algebraic Properties Even Odd Functions

An even function is one in which the graph crosses the y-axis at two points that are an equal distance from the origin. An odd function is one in which the graph crosses the y-axis at one point that is an equal distance from the origin.