Most transponders operate on a bent pipe (i.e., u-bend) principle, sending back to Earth what goes into the conduit with only amplification and a shift from uplink to downlink frequency.
This type, called a "regenerative" transponder, is more complex, but has many advantages, such as improving the signal to noise ratio as the signal is regenerated from the digital domain, and also permits selective processing of the data in the digital domain.
Original analog video only had one channel per transponder, with subcarriers for audio and automatic transmission-identification service ATIS.
In a transponder the transmit carrier frequency is derived from the received signal.
The frequency linkage allows an interrogating ground station to recover the Doppler shift and thus infer range and speed from a communication signal without allocating power to a separate ranging signal.