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Math Help - Help me define this curve!!!!!

  1. #1
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    Help me define this curve!!!!!

    What is the equation of a curve like this (constant then an inflection then straight again)? Thanks in advance.

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  2. #2
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    If you want the function to be smooth then one which approximates the shape you drew is a sigmoid:

    <br />
f(x) = \frac{1}{1+e^{-x}}<br />

    This function has a range of (0,1) but is not constant anywhere (though you can tighten up the function to make the derivative very small as x goes away from 0)

    You can also define such a function peicewise if you want the function to be constant on some intervals.
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  3. #3
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    Thanks!

    Thats great. How can I move this so it is all above 0 in the x plane?
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  4. #4
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    Shifting a function up (or down) by a fixed amount can be done by adding (or subtracting) a constant from the function. The sigmoid function is already above the x=0 line in the plane since
    <br />
x \rightarrow \infty, <br />
f(x) \rightarrow 1<br />

    while

    <br />
x \rightarrow -\infty, <br />
f(x) \rightarrow 0<br />

    To shift a function left (or right) change the input by a constant.
    exp:
    f(x) shifted to the right by 5 is f(x-5)
    f(x) shifted to the left by 5 is f(x+5).
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  5. #5
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    Quote Originally Posted by hadmatter View Post
    What is the equation of a curve like this (constant then an inflection then straight again)? Thanks in advance.
    Maybe you can try:

    f(x) = \frac{\pi}{2} + \arctan(8x)
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