Prove that if the function $f: \mathbb R \to \mathbb R$ is an odd degree polynomial, for every number $y ∈ \mathbb R$ there exists such a number $x ∈ \mathbb R$ that $f(x) = y$. Prove that this is not true for any even polynomial.
I have trouble with this proof. I don't know how to write it for any degree of polynomial. How can I correctly prove it?