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?

Well I'm guessing words of negation would be ones like not, did not, does not, was not, etc. So yes you have not used any words of negation in your answer. But it certainly is not correct. 
We are asked to negate the statement "$f$ is not an increasing function". Think about what should be satisfied for the statement to be wrong. Yes it would be wrong if $f$ is decreasing. But $f$ does not have to be decreasing. 
So your key word in the given sentence is not. See what you can do with it. 
