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Asked: 2026-06-12T15:37:50+00:00

I have number x=[0,n], where n>0. I want to construct a function y=f(x) such

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I have number x=[0,n], where n>0.
I want to construct a function y=f(x) such that the value increase slowly from 0 and increase very fast when approaching n, and when reach n, y is infinity. What is a good function to model this?

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  1. Editorial Team

    1/(n-x) - 1/n will work.

    There are plenty of other functions log, atan, x^(-k),… that goes to infinity at some point.

    a^y is another set of functions with fast grows – maybe more suitable for coding as it can reach arbitrary large (but finite) values.

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