Denote a distance between an object and a lens as O, and the distance between an image and a lens as I. It is known that
[From this formula we see that, as stated on the picture, when O is between F and 2F, I is greater than 2F (2F for O=2F and more for a smaller O).]
When O becomes smaller, I becomes larger. This is the first change that occurs.
The second change is that the size of an image also increases when the distance between an image and a lens increases. As you may see from the given picture, when an object moves towards a lens, the ray which goes from the upper point of an object through the lens' center becomes more inclined to the lens' axis. And the point of intersection moves not only further but also down.