Question

is the function even, odd, or neither. determine algebraically.

f(x)=-4x^3+4x

Answer 1

Plug in -x for x, and if the function is the same as it started it out it is even.
If it is the exact opposite it is odd.
If it is neither of the two above you put neither.

Answer 2

So.
f(x) = -4x^3 + 4x
f(-x) = -4(-x)^3 + 4(-x)
Simplify.
f(-x) = 4x^3 - 4x
It is the exact opposite so this function is odd.