Gamma transfer function – ‘The way I see it’

I have been trying to understand the gamma transfer function. I do not really have a mind for math but let me give it a shot anyway and maybe someone can tell me if I am heading in the right direction. Are the following statements true?

The prescription of my glasses, or contact lenses, can be thought of as representing my own personal gamma?

Gamma would be analogous to the 75ohm impedance matching transformer used to couple my coaxial cable to my TV.

The ‘gamma’ is a value used by the ‘gamma transfer function’ to couple two nonlinear devices?

Each time graphic information is moved from one device to another, linear or nonlinear, a gamma transfer function is applied.
The transfer from my camera to my raw utility would require a gamma value even if I am not aware of it.

The transfer of the same data from the raw converter to the color space of my editor would require another gamma.

The transfer of the same data from my working color space to my computer monitor uses a gamma transfer function – as define by my Adobe gamma control panel, i.e. the 2.2 PC standard.

The various methods of rendering intent – perceptual, absolute, relative and saturation – differ from one another by using a different gamma transfer function?

The ‘Levels’ and ‘Curves’ dialogs in CS2 are breakouts to the gamma transfer function.

There’s nothing magic about gamma. First you need a foundation in mathematics to know what a function is (mapping an input value to an output value), and what an exponential function is. If you used to know this, here is a good source for review, as well as basic knowledge. < http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_alge bra/col_alg_tut5_ratexp.htm>
The gamma transfer function is defined as f(x) = x **(1/gamma) . Once you have that as your starting point, you can be on firm ground as far as generalizations about what gamma does and how it is used. For example, levels and curves do not use an exponential function. So they are not examples of the gamma transfer function.
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I have been trying to understand the gamma transfer function. I do not really have a mind for math but let me give it a shot anyway and maybe someone can tell me if I am heading in the right direction. Are the following statements true?

The prescription of my glasses, or contact lenses, can be thought of as representing my own personal gamma?

Gamma would be analogous to the 75ohm impedance matching transformer used to couple my coaxial cable to my TV.

The ‘gamma’ is a value used by the ‘gamma transfer function’ to couple two nonlinear devices?

Each time graphic information is moved from one device to another, linear or nonlinear, a gamma transfer function is applied.
The transfer from my camera to my raw utility would require a gamma value even if I am not aware of it.

The transfer of the same data from the raw converter to the color space of my editor would require another gamma.

The transfer of the same data from my working color space to my computer monitor uses a gamma transfer function – as define by my Adobe gamma control panel, i.e. the 2.2 PC standard.

The various methods of rendering intent – perceptual, absolute, relative and saturation – differ from one another by using a different gamma transfer function?

The ‘Levels’ and ‘Curves’ dialogs in CS2 are breakouts to the gamma transfer function.

Thanks,
Ron