Recently I've learned many different names for different types of functions... but I've been wondering, is there a name for this type of function?
$\sqrt{x - x^2}$
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3$\begingroup$ I don't think that looks like a semicircle. $\endgroup$– Jonathan HebertJul 3, 2015 at 1:31
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5$\begingroup$ @JonathanHebert But it is, as it is $\sqrt{ (\frac12)^2 - (x - \frac12)^2}$ $\endgroup$– jxnhJul 3, 2015 at 1:40
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1$\begingroup$ Unless you use numbers between 0 and 1 for x, I think the results are imaginary numbers. So this isn't the semicircle function. $\endgroup$– RK01Jul 3, 2015 at 1:44
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1$\begingroup$ You mean to write $\sqrt{1-x^2}$, so people are tring to point out to you that you have written the wrong expression. $\endgroup$– A. Thomas YergerJul 3, 2015 at 1:55
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1$\begingroup$ I can't think of anything beyond "algebraic function" that names that - and that's a very wide class of functions (including anything writable with radicals, sums, and products). I'd just call it a semicircle. $\endgroup$– Milo BrandtJul 3, 2015 at 1:58
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1 Answer
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There are lots and lots of different functions, and there is no name for most of them. There are some classifications and descriptions that can be useful to describe a function; for example your function is an algebraic function and a square root of a polynomial and its graph (over the interval $[0,1]$) is a semicircle. Apart from very few examples (the sine function, the exponential function, the characteristic function of a given set…) you should give a formula if you want to refer to that particular function. Names (consisting of words) are good for describing functions, not for identifying them.
answered Jul 4, 2015 at 10:29