I'm not sure what this is exactly asking Without using words of negation, write the meaning of : "f is not an increasing function"
I did:
$$"f\ is\ not\ an\ increasing\ function" \ \equiv\ "f\ is\ a\ decreasing\ function"$$
Is this what it's asking or am I completely missing it?

What if you were asked to write the meaning of, "$f$ is an increasing function"?
I think the words "for all" might appear when the meaning of that term is written out in full.
Then you could use the fact that $\lnot\forall x.P$ is equivalent to $\exists\, x.\lnot P$
(but of course in your exercise you have to write $\lnot P$ without using the word "not").
