RPM's not going over 2,000-2,500.

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I hope someone will understand what is going on and can offer some help.

I have an 06 LS Sedan, automatic. Engine will start and idle normally but after a while can go up to about 1,200 rpms and become shaky when idling(at this point even if floored, the rpms will not go over 2,000-2,500. Most times this can be temporarily resolved by shutting off the engine and cranking it back up.

Once idling is back to normal, when put into gear, I have to floor it so that it can move or else one of two things happen...1) the car will stall, or 2) it will react as if i am not stepping on the gas. And when I floor it, it will have a delayed response.(not that I'm expecting to peel out.) But even then it's still delayed. If I reach a steady speed, for example 45 mph or any other speed higher than that, I cannot coast or slow down or it will go into that funk I spoke of earlier where the engine will not pick up rpms. At that point I have to shut off the engine, wait a few seconds and will start right up idling normally and start the process all over again. When I do get it to go without having to slow down the engine runs smoothly as if nothing is wrong.(but I must watch out with slowing down.)

I recently have been going through some financial hardships so I am trying to keep the fix as affordable as possible.

ANY HELP would be GREATLY APPRECIATED! Thanks in advance.