## Notation

Functions are labelled by letters – generally though in fact any may be used, Greek letters too. Each function has an associated argument. The function is defined by what it does to the argument.

The argument of is the argument of is and the argument of is Not that it is not the action of the function on that defines the function, but the action of the function on the argument.

If then and We can label all of these by and it is understood that squares whatever is put into it. The graph of therefore is only well understood when the argument is and we can associate with the function a set of points If the argument changes, the graph of will change if the – axis remains the – axis, but we can change the labelling of the – axis in the same way to preserve the shape of the graph. Suppose that we change the argument of from to Keeping the -axis unchanged would have the effect of moving the graph 4 to the right, but if we changing the labelling of the – axis from to this is not necessary. This is shown below for the function  Note that the function squares the argument and subtracts 3, so  