Normalizing a function

  • Thread starter maxtor101
  • Start date
  • #1
24
0
Hi all,

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

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

How would I go about doing this?

Thanks for your help in advance!
Max
 

Answers and Replies

  • #2
eumyang
Homework Helper
1,347
10
Hi all,

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

And I wanted to alter it such that the max value of [itex] p(x) [/itex] 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 [itex] p(x) = \beta \cos(\pi x)[/itex] (before changing p(x))?
 
  • #3
24
0
Well yes, the maximum value would be [itex] \beta [/itex] and the minimum value would be [itex] - \beta [/itex]..
 
  • #4
42
2
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([itex]\pi[/itex]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([itex]\pi[/itex]x) + 1)
 

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