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.

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! What? No Can't say because given info isn't enough. Yes

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