0
$\begingroup$

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 $l\leq f(x)\leq h$?

  • 1
    I'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
  • 0
    What 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
  • 0
    @Andrew no, I'm trying to perform a function on x so that it falls within the interval.2012-06-15
  • 0
    @scottm: I have edited your post. Does it match what you are trying to ask?2012-06-15
  • 0
    @CameronBuie yes, thanks2012-06-15
  • 0
    Draw 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

3 Answers 3