Does the function

$$f(x) = \frac{1}{1 + x}$$

have a recognizable name?

For example a related function with a recognizable name is the logistic function, defined by:

$$l(x) = \frac{1}{1 + e^{-x}}$$

Note: By the way I am quite happy with functions without name.... except when I have to write code for a program, then I wish for nice names.

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    $\begingroup$ Suggestion: we call $f$ the Fred-function. $\endgroup$ – Fred Jun 22 '18 at 9:38
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    $\begingroup$ I am happy that not every function has a name. Otherwise Mathematics would have scared me off :-). $\endgroup$ – Kavi Rama Murthy Jun 22 '18 at 10:08
  • $\begingroup$ geogebra.org/m/JMVCbBjQ $\endgroup$ – Amarildo Jun 22 '18 at 10:42
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    $\begingroup$ @KaviRamaMurthy: there are uncountably many different functions, so not all can get a name. You are safe forever. $\endgroup$ – Yves Daoust Jun 22 '18 at 10:43

This is a homographic function.

As a curve, it is also an equilateral hyperbola.

  • $\begingroup$ These are properties of the function, but they are not names of it because there are many other functions to which they apply. You could also say this is a rational function, an analytic function, and many other adjectives... $\endgroup$ – Rahul Jun 22 '18 at 12:00
  • $\begingroup$ @Rahul: I disagree. When you say "an exponential function", you unambiguously mean a function of the form $ab^x$. This is not a property. You will find many posts about the homographic function. $\endgroup$ – Yves Daoust Jun 22 '18 at 12:05
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    $\begingroup$ Fair enough. Upon further consideration the boundary between "name" and "property" is a bit fuzzy; answering "what is the name of the function $3x^2+2x+5$?" with "it is a quadratic polynomial" feels unsatisfactory, but answering "what is the name of the shape $(x-3)^2+(y-2)^2=5^2$?" with "it is a circle" feels perfectly correct. $\endgroup$ – Rahul Jun 22 '18 at 12:31
  • $\begingroup$ @Rahul: I also made the distinction between the function and the curve. I (personally) would call $3x^2+2x+5$ a quadratic function and wouldn't be bothered by a parabolic function. $\endgroup$ – Yves Daoust Jun 22 '18 at 12:41
  • $\begingroup$ @Rahul: I (still personally) consider that $x$ and/or $y$ translations and/or scalings do not change the nature of the function (say a linear function or a sinusoid). And curves are invariant to similarity transforms (but not necessarily to general affinities). $\endgroup$ – Yves Daoust Jun 22 '18 at 12:47

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