I am relocating my toilet (3 ft ). The current drain is 3" copper. How do I connect the PVC to the copper pipe?

I use a adapter that is sweat on to the copper. I do not know if there are 3 inch compression fittings that will do the same thing. There are also rubber adapters available. With those you use clamps. Check home depot/lowes

"How do I connect the 3" PVC to the copper pipe?"
HVAC gave you a good answer. Let me give you one that doesn't involve soldering on a adapter.
From your local plumbing store pick up a 3" No-Hub Band. You may also use a Fernco Neoprene Coupling but the No-Hub Band will give you more rigidity.
Good luck, Tom

I'll give the no hub adapter a shot.