Simple math question: [closed]

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I have a simple question.

I have two values MIN and MAX. Then i have a series of values (X) that can be between 0 and +infinity.

Now I want to have an algorithm that maps each value x of X into the range between MIN and MAX.

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Here's one that just uses basic arithmetic (no atan or exp):

MAX + (MIN − MAX) / (1 + x)

If you need to vary the shape of this conformal mapping, try

MAX + (MIN − MAX) / (1 + f(x))

for any positive function f (for example f(x) = kx or f(x) = √x or ...).

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MIN + atan(x)*(MAX-MIN)/(PI/2)

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Assuming you want a monotonically increasing function:

MAX + (MIN - MAX)*exp(-k*x)

Where k is a rate factor that determines how quickly the mapping approaches MAX.