I am just starting out with this and and I'm just testing how easy it is to have an object move from left to right on a loop smoothly. (Easing in/out at each extent left and right)

However, I've been trying for 3 HOURS and I cant get it to work! My movement is all jerky and broken no matter what transition curves I seem to put on the keyframes. The only thing i can get working is if I assign linera transition curves but then obviously the movement is not smooth at each extent.

My 1st frame is in the center point of the animation. See below for my current setup..

All the tutorials I can find don't seem to just address these kind of basics...