Even, odd, neither question?

Question

i already know that f(-x) = f(x) is even and that f(-x) = -f(x)

but how would you determine the following equations?

explain why it is even, odd, or neither

f(x) = x^2 - x

f(x) = x^3 + 3(x^2)

f(x) = x^4 +2(x^2)

Answer 1

1) f(x) = x^2 - x ==> neither

demonstrate with f(2) = 2

f(-2) = (-2)^2 - (-2) = 6

neither even nor odd

2) f(x) = x^3 + 3(x^2) ==> neither

demonstrate with f(2) = 20

f(-2) = -8 + 3(4) = 4

neither even nor odd

3) f(x) = x^4 +2(x^2) ==> even

f(2) = 24

f(-2) = 24

f(2) = f(-2) ==> even

(this is a demonstration, not a proof... for the proof, you would use x and -x, not a number, but it's usually easier to see with numbers)