Range scaling function

A function returns a value between 0.0 and 1.0. I want now to apply a scaling function on this result so that I get a value between -500 and 500.

The transition should not be linear but adaptable - that is for example I want to achieve that a value gets transformed within the range [-500,0] is two more times frequent than within the range [1,500].

I've seen a similar question Range scaling problem but there a more linear transformation is discussed.

Thanks a lot for any help on this matter!

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If $g(t)$ is your function with values between $0$ and $1$, then you might want the function $1000g(t)^\alpha -500$, where $\alpha$ is an adjustable parameter. –  Guess who it is. Apr 28 '12 at 14:54
Yes, thx α = 2 is simply what I need currently –  Hawk66 Apr 29 '12 at 8:43

If $g(t)$ is your function with values between $0$ and $1$, then you might want the function $1000g(t)^\alpha−500$, where $\alpha$ is an adjustable parameter. – J. M. Apr 28 at 14:54
Yes, thx $\alpha = 2$ is simply what I need currently – Hawk66 Apr 29 at 8:43