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I'm looking for the rough "parent function" of the following graph.

The graph has a vertical asymptote and a horizontal asymptote. It is most similar to f(x) = ln(x), but more "compressed." Anyone know a rough function for this equation I'm trying to describe?


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Something like $y= 1- e^{-ax}$, $a>0$. –  David Mitra Feb 16 '13 at 16:05
That's very close to what I'm looking for. Does the horizontal asymptote approach 1? edit: I see you put in an extra variable a, which I assume controls the value of lim -> inf f(x). –  user61195 Feb 16 '13 at 16:08
Yes. It does not have a vertical asymptote, though. But, by taking $a$ large, you can make the portion of the graph in the first quadrant near the $y$-axis as close to the $y$-axis as you wish. –  David Mitra Feb 16 '13 at 16:09
EDIT: That function works. Thanks David. –  user61195 Feb 16 '13 at 16:10
If you want both vertical and horizontal asymptotes, you can try $1-a/x$. –  Rahul Feb 16 '13 at 16:38
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