Simple transformations don't have to be unique

If f(x)=x this can be considered as both f=f(x+4) (translate left by 4) and y=f(x)+4 (translate up by 4)

Consider y=¼x²

If f(x)=x² then this is y=¼f(x) (vertical compression by 4) or y=f(½x) (horizontal stretch by 2)

Consider y=4e^x

If f(x)=e^x then this is y=4f(x) (vertical stretch by 4) or y=f(x+ ln 4) (translate left by ln 4)