What does "saturate" or "saturation" mean in relation to functions?

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I am reading:

And the author uses the term saturate a lot in relation to functions. What does that mean?

For example:

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1 Answer

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It means that the function changes over some range but then changes less and less as it approaches a limit, the saturation limit. Much like a solution gets saturated and doesn’t take up any more solvent beyond a certain point no matter how much you put in. The sigmoid is a typical example – it saturates in both directions as you move away from the centre. Another example is $1-\mathrm e^{-x}$, which saturates to $1$ as $x$ increases.

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