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

[maxtor101]

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

 

[eumyang]

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))?

 

[maxtor101]

Well yes, the maximum value would be $\beta$ and the minimum value would be $- \beta$..

 

[dsanz]

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($\pi$x)
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($\pi$x) + 1)

 

[CellCoree]

Hello Max,

Normalizing a function means scaling it so that its maximum value is 1 and its minimum value is 0. In order to do this, you can use the following formula:

p(x) = \frac{p(x) - \min(p(x))}{\max(p(x)) - \min(p(x))}

In your example, this would mean dividing your function by its maximum value. So, your normalized function would be:

p(x) = \frac{\beta \cos(\pi x)}{\beta} = \cos(\pi x)

This normalized function will have a maximum value of 1 and a minimum value of 0, as desired.

I hope this helps! Let me know if you have any other questions.

Best,