Be careful about using the FasTrak transponder installed in the rental car. The rental agency's fee for using it might be more than what you would save by using the carpool lane.
My advice is to cover it in the box it's installed in and just pay cash. Beware that ALL of the toll booth lanes have FasTrak readers installed, not just the FasTrak/carpool-only lanes, so you'll still need to cover it up if you decide to pay cash.