Odd Even Functions

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

Prerequisite for this articles is listed below.

• Intercepts and Symmetry of Graphs
• Functions
• Graph of Functions

The function is even function, if for every x in domain of .

$f(–x) = f\left(x\right)$

for example,

Let be a function where

$f\left(x\right) = x^2$

Let us put some values for , 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 values is equal to .

 

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

Odd Functions

The function is odd function if for every in the domain of .

$f(–x) = –f\left(x\right)$

Consider the following table of points for the function .

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 is .

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

Related Articles:

• Cartesian Plane
• Linear Equations
• Increasing, Decreasing and Constant Functions