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Exponential Function

e^x, the function that is its own derivative, strictly positive and growing multiplicatively. Sigmoid, tanh, and softmax are all built from it.

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Graphing Exponential Functions With e, Transformations, Domain and Range, Asymptotes, Precalculus

Exponential functions possess a horizontal asymptote determined by the vertical shift constant in their transformed equation $y = k \cdot b^{x-h} + v$, which dictates that the domain is always the se…