One way to see
An object at 2f will have an image at 2f
An object a f will have an image at infinity (further than 2f)
So, as the object moves towards the right, the image also moves
towards the right. Vice versa, as the object moves towards the
left, the image also moves towards the left.
The reason being, when you are closer to the lens, the emerging
rays are intersects at an angle that is smaller, hence it will be
at a further distance (draw out to see)
And why is because the one day that goes through the centre of the
lens is now 'steeper' (draw out to try as well!)