Odd Even Functions

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.

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) = x2

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).

 

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 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).

Odd Functions
Odd Functions

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

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