Is my transmission slipping?

Sounds like you gotta broken motor mount to me. If you want to check yourself, Just shut your car off, leave it in park, Open your hood, Grab your front bumper and push back and fourth the whole car should be be moving now and you will see the engine rocking back and forth. If you look down at the bottom center behind the radiator, you will see the motor mount. If you look at it closely with a flash light you can see its got big cracks it the rubber that isolates the engine and keeps the engine still. There is another one in the back of the engine but you can't see that one unless your under the vehicle. If the engine is rocking back and fourth like that, then when your driving and you let off the gas then you get the chugging feeling. When you shift to drive and reverse the motor is moving front to rear you get the CLUNK. Also start it, Open the hood have a freind shift from drive to reverse, look at the engine is it about to jump out of the car??