>> Functions can be classified according to even and odd. And the even and odd notion for functions is related to the idea of symmetry. Now symmetry can occur in three different ways, symmetry about the X axis, Y axis, and origin. Here is an example of a graph which is symmetric to the Y axis and symmetry is fundamental the idea that we could fold along our line of symmetry. In this case the Y axis and the graph which fold on to itself. Now the equation related to this graph is Y equals X squared minus 2. We can evaluate for Y axis symmetry by making a certain replacement within the equation. Now that replacement can be evaluated or we can understand the nature of it by understanding this folding idea. If this is a point XY that is on the graph then notice that when fold, we fold right on to a point which is negative XY. So anytime a point XY is on the graph a point negative XY is on the graph. And so the evaluation algebraically involves taking the equation, replace X with negative X and we should have an equivalent equation. Alright, that's the notion. So we replace X with negative X. We evaluate. This becomes Y equals X squared minus 2. Oh, happy days. It's the same thing we had before so we determine that we have this Y axis symmetry. Now look at it in terms of function notation though. F of X is X squared minus 2. F of negative X, you see, what do we have right here? You see this? This is--if we're talking about F of X for this then when we replace X with negative X in the same function, this is really F of negative X. And F of negative X turns out to be the same thing as F of X. And if F of X is Equal to F of negative X then we have an even function. Then F of X is an even function.