This was the input, to use formulas to generate the vector labels

How to save this graphic as an image file:  Clicking on the graphic seems to allow editing it.  Click on the sidebar for the cell containing it, then File->Save Selection As

Clear[f]
f[x_] = E^(- x^2)
Manipulate[ Plot[{f[x], f[x -3]}, {x,-r, r}], {r,  1, 30}]

E^(-x^2)