Explanation of Map Range

I still can’t quite get a handle on the math behind the map range, and it keeps coming up in this video so this seems like a good place to ask. Could you breakdown for me the mathematical consequences of each input and output?

For example, if I hook a black and white gradient texture up to a map range, I would think that lowering the “From Max” would make the maximum value on the texture lower, i.e closer to 0, and therefore make more of the darker colors darker. My thinking is it’s taking the maximum possible value and setting it closer to 0 by lowering it, but lower “From Max” makes a larger area brighter. Why is this happening? Is it condensing the “scale” of possible values, squishing values into higher levels of brightness?

Thanks for any input you can provide.