How do you know if something is a state function? I know Internal Energy (U) is a state function since it is the sum of energies, which is constant at a given time.
However I don't know for sure if $\Delta$U is a state function. I know that $\Delta$U$= U_{final}-U_{initial}$, and so any path from final to initial will yield the same $\Delta$U. So by this definition any $\Delta$ function should be a state function.
As a result I would expect Heat ($q$) to also be a state function since $q=\Delta$TE, but this is not the case.
Where am i going wrong in my understanding? I understand the "altitude" analogy, however i need a more technical definition with chemistry terms. 
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