OK, this is an odd request, but is there some way or existing list of monotonic decreasing functions? The limitations I have are:

- f is monotonic and decreasing.

- f(0) = a, a is a real constant; f(1) = 1 ( or simply, passes through (0,a) and (1,1) )

- Cartesian equations, most preferably.

I thought it would be useful if there was such a thing (so there probably is), even if it's a software, like those curve fitting ones which have a predefined set of functions, just that here I'm (edit: interesting -> interested) in threading through the exact points. Reason being, I've written a code that does wonders with any input function for problems in fluid dynamics, but I'm having trouble thinking of inputs to test it out with when I have these limitations. Here's two fairly easy ones which I have thought of so far:

y = (1-a)(x-1) + 1

y = (a-1)(-10x^3 + 15x^4 - 6x^5) + a

Thanks in advance!

- f is monotonic and decreasing.

- f(0) = a, a is a real constant; f(1) = 1 ( or simply, passes through (0,a) and (1,1) )

- Cartesian equations, most preferably.

I thought it would be useful if there was such a thing (so there probably is), even if it's a software, like those curve fitting ones which have a predefined set of functions, just that here I'm (edit: interesting -> interested) in threading through the exact points. Reason being, I've written a code that does wonders with any input function for problems in fluid dynamics, but I'm having trouble thinking of inputs to test it out with when I have these limitations. Here's two fairly easy ones which I have thought of so far:

y = (1-a)(x-1) + 1

y = (a-1)(-10x^3 + 15x^4 - 6x^5) + a

Thanks in advance!

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