Shifting Concept

But mathematically, this is incorrect, since the change is inside the function, not outside. If it were outside the function, I would agree with you. 

The statement should be reversed. In fact, if we change x variable inside any function, we will shift its graph to the opposit direction of the sign. That means, if we substract 3 from x inside a given function, we will shift the graph to the right, and vice versa. 

It needs adjustment!