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Is it possible to have a not piecewise function that can be written with a relation (any function that can be written as $y=f(x)$ for all $x$ that turns out to be constant in an interval of $x$? Say, for example, a function $y=f(x)$ where $y$ is constant for $0<x<1$.

Andibadia
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How about $f(x) = \left(\dfrac{4^x\cdot \Gamma(x+1)\cdot \Gamma\left(x + \dfrac{1}{2} \right)}{\Gamma(2x+1)}\right)^2$?

This function is actually constant over all complex numbers, not just a specific interval. It always equals $\pi$.

SlipEternal
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  • If this answer does not satisfy, how about a little more information about what you are looking for? – SlipEternal May 03 '18 at 19:51
  • Thank you! It isn't exactly what I was looking for (I was hoping to find a function based on real numbers, since I was thinking of a hypothetical scenario, where the function I'm looking for returns the time needed to go from a point A to a point B depending on the departure, and I wanted to find a function that implied that for an interval of the departure time, the total time needed would be the same), but I didn't know of this and it's quite interesting – Andibadia May 04 '18 at 03:38
  • It is constant over all real numbers, as well. The real numbers are a subset of the complex numbers. – SlipEternal May 04 '18 at 13:21