It hesitates when put in reverse. I have to give some gas before it will engage

What is your question?

At first the engine would rev high so I would shut it off and restart then would put in reverse and it wouldn't move or engage until giving it gas. Can you tell me what the problem is? Not sure if it needs a new tranny or if its and idle sensor. Mechanic said it doesn't have a vacuum leak. The problem seems to happen after I've driven it for awhile