Ok, I feel really stupid for asking this, but what is the name and general form of an equation that would be like one graphed below?  The red line is the graph and the blue lines are two horizontal asymptotes. 

It almost sort of like an inverse tan, but I was wondering if there was another equation that would graph to something similar.

I dont know much about graphs. My attempt failed

And using parser's I think instead of
(1/(1+e^X))

-(1/(1+e^X)) makes it go in the right direction even though I have no clue what it really does

No it was
(something)log(x-(something))+(something)
I just randomly guessed since when you said "logistic", I interpreted "use log" for it

I dont know much about graphs. My attempt failed

And using parser's I think instead of
(1/(1+e^X))

-(1/(1+e^X)) makes it go in the right direction even though I have no clue what it really does

Or 1/(1+e^(-X)), the usual form of the logistic function.
[wikipedia]Logistic function[/wikipedia]

looks like a logistic function to me.
(1/(1+e^X))
where e is [2nd] [divide]


(but don't graph with zstandard, use zoomfit)

Sweet, a logistic function fits the graph (and makes sense within the context of the problem I'm working with).  Thanks!