# Name for function of the form $f \colon (0, 1) \to (0, 1)$

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