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What is the function to the following graphs? I am just looking for a rough estimate. It doesn't need to match the exact graph. enter image description here

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maybe $ \ x^ {-n } \ $ could do the job? – sigmatau Jul 22 '13 at 22:24
Yeah that is close. But since it is only in the first quadrant, is there a way to express that in the function? – ustroetz Jul 22 '13 at 22:25
They can't be $x^{-n}$ because the two lower graphs cross each other and the top graph appears to have a minimum around $58$ - I'd quote colours if I were not colour-blind. – Mark Bennet Jul 22 '13 at 22:29
@user1738154 well, all we see is the first quadrant .Who knows what kind of strange things are happening on the other quadrants (: – sigmatau Jul 22 '13 at 22:33
Nothing is happening on the other quadrants. That is why I only posted the first quadrant. – ustroetz Jul 22 '13 at 22:51
up vote 1 down vote accepted

It depends on what you think is happening to the right. Clearly it goes to infinity for $x=0$ so there is a denominator of $x^n$. If they each approach a constant, I would say each is $a+x^{-n}$. The fact that the corner on the green one is sharper than the others would say it has a greater $n$. I would collect some points from each graph, estimate the asymptote, and see what $n$ fits best.

If you think the rise of the red one toward the right is real, you could add a term $+bx$ for a rather small $b$.

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