Let E be an even function and O be an odd function. Determine the symmetry, if any, of the following function.

E (Dot) O

Remember that E (-x) = E (x) for all even functions (and all real numbers for x) and that O (-x) = - O (x):

So for each let's plug in - x into the resulting equaiton and see what comes out:

1) F (x) = E (x) * O (x)

F (-x) = E (-x) * O (-x) = E (x) ( - O (x)) = - E (x) * O (x) = - F (x), which means that F (x) is

an ODD function