I have fed a series of numbers into a graphmapper (without using Range) and I am trying to understand the correlation between the input and the output.
Since I am not using Range as the input (Hence no vertical division marks on the graph), I am wondering how the Graphmapper remaps the input to arrive at the resulting outputs.

Any help to enlighten my wonders would be much appreciated!

Basically it is f(x) = y, where x is the input (X-axis) and y is the output (Y-axis). To manually edit a function f, you need to work in a domain of x (from x0 to x1), you can put any value there, but normally you put a value inside that working domain (normally from 0 to 1) because that way you get an expected value, visible in the graph drawing. On the other hand you also need an output working domain (from y0 to y1) to map the result of the function y to a domain you are interested in. Normally this is also from 0 to 1, and when this is the case, if the graph cuts in the middle of the height, for that input/x will give a value of 0.5.

The vertical lines correspond to the input value. If your function works between x0 and x1, then your input values should be between x0 and x1. However, these lines do not appear when there are too many input values, to avoid too many red lines.

The common use of the Range component is mainly for convenience, as by default it returns a list of numbers between 0 and 1, which is the default domain of the GraphMapper at X. If you use the Series component instead, you either have to remap these values between 0 and 1 or change the X domain of the Graph mapper to the domain of your numbers.

Here you have a version of the component with the domains as inputs: