Why is there a S-shaped curve (concave function) in gain domain?

The S-shaped curve (concave function) in gain domain is typically seen in gain functions like logarithmic gains, which refer to how an input affects the output or the gain of a system. This shape of function is concave because the increases in the input do not result in equal increases in the output; you need greater increases in the input to see an increase in the output. The S-shaped curve reflects this gradual plateauing of the gains, with greater amounts of input either not having a significant effect on the output or plateauing the output at some point, rather than producing an exponential increase in the output.