# What do the coordinates in a RGB-Curve mean?

Is the curve a representation of a function which describes y = f(x) where x is the input as composite or R,G.B channel and y is the result where x and y are in the range 0..255?

In case that is true, how does the vertical graph (D) perform a posterization as described in the Documentation on RGB curves ? A) Lighten B) Negative C) Decrease Contrast D) Posterize

The coordinate range of the RGB curves is [0, 1]. The RGB values in Blender are always in [0, 1] range, where 0 is is no intensity and 1 is full intesity of the color channel. Otherwise you are correct. The curve represents a function which maps input values (x axis) to output values (y axis).
If you apply this curve to an image the R, G and B values of every pixel are mapped to either 0 or 1, resulting in 2³ = 8 possible colors. Reducing the number of possible colors in an image is often called posterization.
If you want posterization with more than eight colors you could add more steps to the curve. Here is an example of a curve that will map an image to 3³ = 27 colors. 