Odd Even Functions

Table of Contents

The graph of equation has symmetry along the x-axis or y-axis. In this article, the symmetry of a graph of function is defined in terms of even and odd function.

Prerequisite for this articles is listed below.

Even Function

Let’s understand the even functions first. The function $y = f(x)$ is even function, if for every x in domain of $f$ .

f(-x) = f(x)

For example,

Let $y = f(x)$ be a function where

f(x) = x^2

The function will square any input value for $x$ and output $f(x)$ . Let us put some values for $f(x)$ , see the following table of values.

x	y = f(x)	point
-2	4	(-2, 4)
-1	1	(-1, 1)
0	0	(0, 0)
1	1	(1, 1)
2	4	(2, 4)

The table shows that any $f(-x)$ values is equal to $f(x)$ .

The graph of even function is symmetric along the y-axis.

Odd Functions

The odd function is different from even function in terms of symmetry of graph of the function. The function $y = f(x)$ is odd function if for every $x$ in the domain of $f$ .

f(-x) = -f(x)

Consider the following table of points for the function $y = f(x) = x + 1$ .

x	y = f(x) = x + 1	point
-3	-2	(-3, -2)
-2	-1	(-2, -1)
-1	0	(-1, 0)
0	1	(0, 1)
1	2	(1, 2)
2	3	(2, 3)

The graph of odd function shows that $f(-x) = x + 1$ is $-f(x)$ .

The graph of odd function is symmetric along the y-axis.