Is f(x) = x³ - 4x even, odd, or neither?

A function is odd when $f(-x)=-f(x)$. Here $f(-x)=(-x)^3-4(-x)=-x^3+4x=-(x^3-4x)=-f(x)$, so $f$ is odd, choice D. Both terms have odd powers of $x$, and every term in an odd function must have an odd power. Choice A (even) would need $f(-x)=f(x)$, which fails: $f(1)=-3$ but $f(-1)=3$. Choice C (neither) applies when the symmetry breaks, for example if a constant term were added. Choice B is wrong because the algebraic test settles the question.