How can I get my fig tree to start growing?

I am about to move and I have a beautiful fig tree in the yard where I am living at now. I cut a piece off of it and put some root hormone on the end and put in the soil like the man at the nursery told me to do, but the leaves are dying, and I really would like a part of this tree before I move. My grandmother started this tree with just a clipping when I was 23 and now I am 38 and we are still eating off of this tree.