2006 Chevy Cobalt car idle jumps and car turns off occasion

My car idle jumps up and down, and when i'm in park I hit the gas for a slight rev. And the idle drops very low and the headlight dim as if the car is gonna die/turn off. Some times i'll star the car and the drive is rough and a few feet later when I stop or slow down or when I go in reverse my car turns off. Especially when gas is low its at its worst. My car sometimes will turn off after I hit a right/left turn and I go to push on the gas and it cuts off. Although everytime it happens it starts right up again