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.

Advertisements

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)
Advertisements

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.

Advertisements

Ads Blocker Image Powered by Code Help Pro

Ads Blocker Detected!!!

We have detected that you are using extensions to block ads. Please support us by disabling these ads blocker.