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January 23rd, 2012, 03:27 PM   #1
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Classes of equations?

How do I find a complete set of equations, or classes of equations, that satisfy the following conditions:

The function must be smooth and connected everywhere.
When the function crosses the y-axis it must have a finite negative value (let us call the absolute value of this value a), and the slope of the function where it crosses the y-axis must be zero.
At some finite positive x-value (let's call this value b) the function must cross the x-axis. At point b the slope must be infinite, and b must be an inflection point.
Finally, the graph should be symmetric about the y-axis.

I know that the following equation satisfies all but the last of these conditions, but I do not know how to identify the class of equations that satisfy them all.

y = (x-a)^(1/b)

Can anyone help?
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January 27th, 2012, 12:50 AM   #2
duz
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Re: Classes of equations?

This is not linear algebra problem.
You could have a try to the function with period 2 and it is
-sqrt(1-x^2) when -1<=x<=1
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January 27th, 2012, 12:54 AM   #3
duz
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Re: Classes of equations?

It should be function with period 4 and
-sqrt(1-x^2) when -1<=x<=1
and
sqrt(1-(x-2)^2) when 1<=x<=3
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