Ok suppose you have f(x)= sin 2x and and g(x)= sin(2x-30)
What would be the transformation? presumably you would all agree it is a shift of 30 in the x direction?
Now if you have f(x)= 2^(4x)
and g(x)= 2^(4x-3)
Why isn't this simply a translation of 3 in the x direction? It is infact a translation of 3/4
( or a stretch..but forget that for the moment)