If you shift a function to the left 4 units, the only thing you are doing to it is moving it. You are not changing its shape or its orientation. A simple example is the parabola y = x^2. The vertex is at the origin. When you shift it 4 units to the right, the new equation is y = (x+4)^2 which shows we have moved the parabola 4 units to the left. Nothing else changes about it.
