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 is even function, if for every x in domain of
.
for example,
Let be a function where
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
.
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.
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