# 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.

The function $y = f(x)$ is even function, if for every x in domain of $f$.

for example,

Let $y = f(x)$ be a function where

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 $f(x)$.

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 $f$.

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 $-f(x)$.

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

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