I'm looking for a name for a class of functions $y = f(x)$ that satisfies the following:

  • $f$ is defined for x in $(0, 1)$,
  • the output $f(x)$ is in $(0, 1)$.

Typical simple examples are:

  • $f(x) := x\quad\quad$ (a linear response)
  • $f(x) := x^{2.2}\quad$ (a 2.2 gamma curve)

It should intuitively represent: what comes out if this goes in? In case of a simple $y=x$ function, the function has no effect.

I'm developing some software where the user has to interact with this type of curve in a 1-by-1 box. I'm trying to come up with names:

  • transfer function (not correct, as this is a term from signal processing, related to transform analysis).
  • response function

Anyone that can come up with a good name for these type of functions?

UPDATE: Some more suggestions I came up with:

  • Unit Function
  • Box Function
  • Unit Box Function
  • Unit Square Function
  • Unit Transformation Function
  • $\begingroup$ I think it depends on the context in which it is used. $\endgroup$ – rubik Jul 28 '17 at 10:47
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    $\begingroup$ Never heard these functions have a name... What about you call them $1$-by-$1$ box functions? $\endgroup$ – Edu Jul 28 '17 at 10:50
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    $\begingroup$ I have the follwing suggestion: call them FRED-functions. $\endgroup$ – Fred Jul 28 '17 at 10:55
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    $\begingroup$ Functions from a set to the same set are sometimes called transformations. $\endgroup$ – Yves Daoust Jul 28 '17 at 10:56
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    $\begingroup$ @rubik: My specific context is a Photoshop like Curves function, like RGB curves, or Luma curve for example. $\endgroup$ – Martijn Courteaux Jul 28 '17 at 11:00

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