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Mathematics-Online lexicon:

Even and Odd Functions

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A function $ f$ is called even if $ f(x) = f(-x)$ , i.e. if the graph is symmetric to the $ y$ -axis.

A function is called odd if $ f(x) = -f(-x)$ , i.e. if the graph is symmetric to the origin.

\includegraphics[width=6.5cm]{Gerade_Funktion_Bild1}   \includegraphics[width=6.5cm]{Ungerade_Funktion_Bild1}

The product of two even functions is even, as is the product of two odd functions. But the product of an even and an odd function is odd.

The sum or difference of functions is of the same type as the functions themselves.

see also:

[Examples]
  automatically generated 4/ 8/2008