We have fabricated carbon-nanotube (CN) field-effect transistors with multiple, individually addressable gate segments. The devices exhibit markedly different transistor characteristics when switched using gate segments controlling the device interior versus those near the source and drain. We ascribe this difference to a change from Schottky-barrier modulation at the contacts to bulk switching. We also find that the current through the bulk portion is independent of gate length for any gate voltage, offering direct evidence for ballistic transport in semiconducting carbon nanotubes over at least a few hundred nanometers, even for relatively small carrier velocities.