Antenna booster

How does the antenna booster work, and why does the tv in the living room get so much better reception than the one in the back room? Also the tv in the master bedroom is slightly better than the back room, but nowhere near as good as the living room

The first thing that comes to mind is bad coax connectors. If this sounds possible, you'll have to test the connectors to see if the grounding shield is contacting the center wire. Use a continuity tester or Ohm Meter.

I'll check the connectors, but does the booster boost all 3 connections? And does it split behind the booster or somewhere near it?