Even and Odd FUNctions

An even function ,f(x)=f(-x), is when the functioned that would be graphed would be symmetrical along the y-axis. For instance normally the graph f(x)=x^2 would be on the 1st and 4th quadrant but with f(-x)=x^2 it is the same graph. An example of why this is would be is if one plugs in a number the input is changed to to its negative so if one plugs in 1 it would turn (-1) but a negative squared is a positive so it would have a different input due to the change but the same output. So f(x)=(1)^2=1 makes (1,1) and f(-x)=(-1)^2=1 makes(-1,1) both of these point are in the Graph of f(x)=x^2 and/or f(-x)=x^2 so this makes f(x)=f(-x) true.

Note:Would be a lot easier to prove if I new how put in pictures but oh well.

An odd function,f(-x)=-f(x), is when a graph is rotated 180 degrees and it still maintains the same graph thus saying that if one chooses a point from the graph then its opposite (x,y) are on the same graph. For in stance lets assume that a graph has the point (1,1) then the point (-1,-1) is on the same graph. An example is the equation f(x)=x it is just a diagnal line that hold the point (1,1) and various others, now when rotated it is still the same line and still hold the same point including,which it always included, the point (-1,-1) and other point that are opposite of the same point.

Note: This is as simple as I can put it and I can barely understand it but again it would be a lot better if I new how to put in pictures.