What is the function to the following graph?

Question

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.

Answer 1

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 $b$.