Even and Odd functions are usually determined through Standard Form, that is the best way, however, what if we wanted to save time hm?
Even Functions
Double negation
An Even Function means that f(x) = f(-x).
for this to be possible, it means that each x intercept has a negative version of it too.
Look at this:
5 and -5.
Thus, each factored polynomial must look something like this:
f(x) = (x-5)(x+5)
each x intecept has a copy of itself but negative too
Another example:
f(x) = (x-7)^2(2x+14)^2
these are (x-7) and (x+7). negatives of eachother so it is Even
Even powers
Another way you can tell is if each factor has repeated powers.
this is a even graph, the formula is:
y=(x-2/3)^2(x-5)^2
This also works because each factor has an even power of 2.
Odd
There is no good method to finding out odds easily. Unfortunately, you will have to keep with the method of first finding f(-x), then finding -f(x) and then comparing to see if both are the same.