A function is said to be an even function if,
and to be an odd function if,
Note that these definitions require D(f) to lie symmetrically about x=0 (ie ). Clearly even functions have graphs that are symmetrical about the y-axis, whilst for odd functions the origin is a centre of rotational symmetry.
Examples are for even, and for odd. Most functions are neither odd nor even. However every function (subject to having a symmetrical domain) may be expressed as the sum of an odd and even function since , which is even + odd.
ie. even + odd.