Stuck

For the function, find whether or not it is increasing, decreasing, even, odd, and/or invertible on its natural domain:

$f(x) = \frac{x}{x^2+1}$

I found that it is odd (graph)

and it is invertible (since all of its outputs are unique)

And I found it is decreasing after putting in some inputs

I think im missing something here... since I got it wrong... any help?

Thanks!