This is probably very simple for some of you, but I can't for the life of me get something that works reliably. Given any positive number, $x$, and a positive high and low value $(h, l)$ what kind of functions $f$ are there such that $l\leq f(x)\leq h$?
How to perform a transformation on a number so that it is between a high and low value?
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linear-algebra
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1I'm not sure that I understand the question. Are you looking for an expression that can be converted to a boolean value indicating whether or not x falls within the specified interval? – 2012-06-15
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0What are the conditions on the function you are loking for? The answer gives one possible solution; another would be $f(x) = (l-h)e^{-x} +l$. Technically, the constant function $f(x) = l$ would work too... The right function depends on the exact problem you are trying to solve. – 2012-06-15
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0@Andrew no, I'm trying to perform a function on x so that it falls within the interval. – 2012-06-15
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0@scottm: I have edited your post. Does it match what you are trying to ask? – 2012-06-15
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0@CameronBuie yes, thanks – 2012-06-15
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0Draw a sketch of the graph you have in mind, and the community will provide you with an analytical expression for an $f$ that approximates your graph. – 2012-06-15