Question

How do you know if `f(x)= -4x^2 + 4x` is an even or odd function?

Answer 1

`f(x)` is neither even nor odd.

Explanation:

A function `f(x)` is even if and only if `f(-x) = f(x)`
A function `f(x)` is odd if and only if `f(-x) = -f(x)`

In this case
`f(-x) = -4(-x)^2 + 4(-x) = -4x^2 -4x != f(x)`

and

`-f(x) = -(-4x^2 + 4x) = 4x^2 - 4x != f(-x)`

So
`f(-x) != f(x)`
and
`f(-x) != -f(x)`

meaning `f(x)` is neither even nor odd.