Asymptotics of a function that decreases as n increases A homework assignment asks me to state the complexity in Big-O notation of the function
$$f(n) =  7n – 3n \log n + 100000 $$

I graphed this function and decreases all the way down to zero nearly its entire lifespan. 
Therefore I concluded that the complexity is bounded by a constant and has the complexity $O(1)$.

Is this correct?

Also out of curiosity, what is the Big-Omega of this function is? The best it could ever run is also O(1). 
What about Big-Theta? I'm having trouble getting my head around these.
If you use suitable definitions, you'll find that your function is in


$O(2^n)$,
$O(n^4)$,
$o(1)$ and
$\Omega(-n^2)$,


among many others. It's likely that the question (implicitly) asks for sharper bounds; I'll leave that for you to figure out.