In d3, if you want to create an axis you might do something like this:
var xAxis = d3.svg.axis()
.scale(x)
where x is a scale function. I understand that the domain of x defines the start and ending values for the ticks. I'm having trouble understanding how the range of x changes the resulting axis. What does the domain map to in the context of an axis.
Think about what one must do to create a visual representation of any data set. You must convert each data point (e.g. 1 million dollars) into a point on the screen. If your data has a minimum value of $0 and maximum value of $1000000, you have a domain of 0 to 1000000. Now to represent your data on a computer screen you must convert each data point (e.g. $25) into a number of pixels. You could try a simple 1 to 1 linear conversion ($25 converts to 25 pixels on the screen), in which case your range would be the same as your domain = 0 to 1000000. But this would require a bloody big screen. More likely we have an idea of how large we want the graphic to appear on the screen, so we set our range accordingly (e.g. 0 to 600).
The d3 scale function converts each data point in your dataset into a corresponding value within your range. That enables it to be presented on the screen. The previous example is a simple conversion so the d3.scale() function is not doing much for you, but spend some time converting data points into a visual representation and you will quickly discover some situations where the scale function is doing a lot of work for you.
In the particular case of an axis, the scale function is doing exactly the same thing. It is doing the conversion (to pixels) for each 'tick' and placing them on the screen.