Am I cubic?

Algebra Level 4

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

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

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

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

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