Am I cubic?

Algebra Level 4

We have a polynomial $f(x)$ which satisfies the following conditions:

$f(1)=4~,~f(2)=3~,~f(3)=4~,~f(4)=7$

Can $f(x)$ be a cubic polynomial?

Note: This problem is original and is inspired by a facebook post.

Yes What? No It can and can't be simultaneously unless I give a proof. It's Schrodinger's

f(x)

. :P BATMAN! The answer is always batman! Can't say because given info isn't enough.