Odd Even Functions

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.

xy = f(x)point
-24(-2, 4)
-11(-1, 1)
00(0, 0)
11(1, 1)
24(2, 4)

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

Even Function F(x) = x^2
Even Function F(x) = x^2

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.

xy = f(x) = x + 1point
-3-2(-3, -2)
-2-1(-2, -1)
-10(-1, 0)
01(0, 1)
12(1, 2)
23(2, 3)

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

Odd Functions
Odd Functions

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


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