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The Sigmoid function is like this: $\frac{1}{1 + e^{-x}}$

Can it be derived by simply scaling and translating the graph of $e^{-x}$ ?

It looks to me as thought you could:

1). Translate it up, by 1

2). Scale it vertically by -1

However, when I draw this out it doesn't look like the sigmoid function?

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$\displaystyle\frac{1}{1+e^{-x}}$ is bounded while any translation or scaling of $e^{-x}$ is not.

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  • $\begingroup$ So are they fundamentally different functions, then? Or can I still go from one to the other by simply restricting its domain (bounding it), scaling and then translating it, as appropriate. $\endgroup$ – COOLBEANS May 10 '15 at 10:09
  • $\begingroup$ Restricting the domain definetly does not help because both are analytic functions. If they coincide on a set with a limit point they automatically coincide on $\mathbb R$, which can't be true since one is bounded there and one is not. $\endgroup$ – Tim B. May 10 '15 at 10:16

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