The value of the logistic sigmoid function cannot be greater than one, and it cannot be less than zero.

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BlackTom AI · Accepted Answer

Consider the statement about the logistic sigmoid function and its value range. 
Option 1 (True): The sigmoid function defined as σ(x) = 1 / (1 + e^(-x)) yields outputs strictly between 0 and 1 for all real x, and it approaches 0 as x -> -∞ and 1 as x -> ∞. This means it never exceeds 1 and never drops below 0, which supports the claim that its value cannot be greater than one or less than zero. 
Option 2 (False): If one thought the function could produce values outside [0,1], they might confuse it with other activation functions or think about complex arguments, but for the standard real-valued logistic sigmoid, the codomain is limited to (0,1). Additionally, while the limits approach 0 and 1 asymptotically, the function never actually attains 0 or 1 for any finite input, which reinforces the stated bounds. 
In summary, the asserted bounds align with the mathematical definition and limiting behavior of the sigmoid, and the only subtlety is that σ(x) ≠ 0 and σ(x) ≠ 1 for any finite x, though it gets arbitrarily close to both. This nuance does not contradict the overall claim about the value range being within [0,1].

QBUS6810 (ND) Week 4 Quiz

The value of the logistic sigmoid function cannot be greater than one, and it cannot be less than zero.

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