Wiktionary
n. (context mathematics English) a mathematical representation of the relation between the input and output of a linear time-invariant system
Wikipedia
In engineering, a transfer function (also known as the system function or network function and, when plotted as a graph, transfer curve) is a mathematical representation for fit or to describe inputs and outputs of black box models.
Typically it is a representation in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant system (LTI) with zero initial conditions and zero-point equilibrium. With optical imaging devices, for example, it is the Fourier transform of the point spread function (hence a function of spatial frequency) i.e., the intensity distribution caused by a point object in the field of view. A number of sources however use "transfer function" to mean some input-output characteristic in direct physical measures (e.g., output voltage as a function of input voltage of a two-port network) rather than its transform to the s-plane.
Usage examples of "transfer function".
The inverting function, for a given observer in a given condition, may be called the lightness transfer function, or LTF.
The result of this transfer function is something that cannot be talked about, not because it is something forbidden, but because it is something indescribable.