this is an example of a even function:
this is an example of a odd function:
Even and odd functions are both similar because they are both symmetric, just in different ways. For example even functions are symmetric across the Y axis, and odd functions are symmetric by its origin(folding over x axis, then y axis) or 180 degree rotations. They are different because obviously one is odd and one is even, but they are also have different patterns when looking at the table of values. Even table of values have two positive set of points, and for the same points its reflected and has a negative x value and the same y value. For example (1,1), when reflected its other set becomes (-1,1). To check if a function is even you have to verify that f(-x)=f(x), for odd functions you have to verify that f(-x)=-f(x). Yes there are functions that will always be even such as x^2, if you verify with the function that it is even then there will be no change to this, and its the same for odd functions. I think I have a pretty good grasp on this unit, but one question would be how do you tell or know if any families of functions are always even or always negative, that wasn't really made clear.