JenniferMurphy
Well-known Member
- Joined
- Jul 23, 2011
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I know this is technically not an Excel question, but there are a lot of people here with better math skills than mine, so I hope this is OK.
I would like to find a family of functions, f(x,m), that meets these conditions:
I thought I had it with quadratics (parabolas), but when m gets close to 0 or 10, the function exceeds the range. Here are the results of the parabolas:
https://www.dropbox.com/sh/hwboo6bb6i40451/AADDz82Ev1oEYycC-0QRNSXBa?dl=0
This is more or less what I want, but with the functions staying within the range.
I would like to find a family of functions, f(x,m), that meets these conditions:
- Maps the domain (0,10) onto the same range and is continuous over that domain.
- f(0) = 0
- f(10) = 10
- f(5) = m; 0<m<10
- f(x) is monotonically increasing. This means that it cannot be greater than 10 or less than 0.
- If m=5, the function is y=x (straight line)
I thought I had it with quadratics (parabolas), but when m gets close to 0 or 10, the function exceeds the range. Here are the results of the parabolas:
https://www.dropbox.com/sh/hwboo6bb6i40451/AADDz82Ev1oEYycC-0QRNSXBa?dl=0
This is more or less what I want, but with the functions staying within the range.