The sigmoid and logistic functions have the same shape, and the logistic function is an example of a sigmoid curve

Question

BlackTom AI · Accepted Answer

The statement asks about the relationship between sigmoid and logistic functions. 
Option 1: True. The logistic function is a classic example of a sigmoid (S-shaped) curve. Specifically, the logistic function f(x) = 1 / (1 + e^{-x}) has the characteristic S-shaped growth, with two horizontal asymptotes and a smooth, increasing transition from 0 to 1. This is the archetype of a sigmoid function in mathematics and statistics.
Option 2: False. If the assertion were false, it would imply that either the logistic is not sigmoid or that sigmoids do not resemble the logistic form at all. However, the logistic function exhibits exactly the standard sigmoid properties—monotonic increase, inflection at the midpoint, and an S-shaped curve—so this option mischaracterizes the relationship.
In summary, the logistic function is widely cited as a quintessential sigmoid function, making the statement accurate.

The sigmoid and logistic functions have the same shape, and the logistic function is an example of a sigmoid curve

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