How Do You Normalize a Function to Have a Maximum of 1 and Minimum of 0?

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SUMMARY

The discussion focuses on normalizing the function p(x) = β cos(πx) to achieve a maximum value of 1 and a minimum value of 0. The initial maximum and minimum values of the function are β and -β, respectively. To normalize, the function is first adjusted by dividing by 2β, resulting in p'(x) = 0.5 cos(πx), which ranges from -0.5 to 0.5. Finally, the function is shifted upward by 0.5, yielding the normalized function p''(x) = 0.5 (cos(πx) + 1).

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maxtor101
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Hi all,

Say if I had a function for example p(x) = \beta \cos(\pi x)

And I wanted to alter it such that the max value of p(x) is 1 and its minimum value is 0.

How would I go about doing this?

Thanks for your help in advance!
Max
 
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maxtor101 said:
Hi all,

Say if I had a function for example p(x) = \beta \cos(\pi x)

And I wanted to alter it such that the max value of p(x) is 1 and its minimum value is 0.

How would I go about doing this?

Thanks for your help in advance!
Max
Do you know the minimum and maximum values of p(x) = \beta \cos(\pi x) (before changing p(x))?
 
Well yes, the maximum value would be \beta and the minimum value would be - \beta..
 
Well a very simple way to do it would be to first "shrink" your range from being -β to β, and making it 1. You can do this by dividing by 2β, and you get p'(x) = 0.5 cos(\pix)
Now your function covers -0.5 to 0.5 so what you have to do now is move its range "up" by 0.5... so you get p''(x) = 0.5 (cos(\pix) + 1)
 

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