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With a basic function like $y = 1/x$ mapped over the first 100 integers I see the curve elbow at around 5.

enter image description here

I want to shift this closer to 100... to "flatten" the curve so to speak, so it grows more quickly on the right of the elbow and less so on the left.

How can I accomplish this?

I've tried things like $y = 1/(x^C)$ where $C$ is some suitable value $< 1$ but all it does is shift the right end of the curve with the elbow at the same place

ekkis
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  • Hello @ekkis, welcome to MSE. Can you please explain in your question (not in the comments) what you exactly mean by "I see the curve elbow at around 8 or 9". At this point, it is not clear what kind of behaviour of the curve $y=1/x$ you are talking about. – Ernie060 Oct 26 '19 at 22:56
  • I've added a picture. they say a picture is worth 1,000 words. the elbow, the inflection point, is now at around 5. I'd like to be able to shift it, perhaps moving it to the right (closer to 39) or up, to make the curve softer – ekkis Oct 28 '19 at 03:49

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