Kind of depends on the system used.
CATV systems will have some DC coupled to each loop, which is to drive line amps at nodes, so they could also use that DC to power a small in-line preamp, such as the one pictured.
DSB [Satellite broadcast] will drive the LNB / LNBF at the "Dish" receiving antenna with DC power, which is coupled to the coax feed [the cable coming from the dish].
As to regular Yagi / Parasitic Yagi antennas used for VHF / UHF television, these two types of preamps can be used - without external power source / coupled DC:
1: Cable Bootstrapping [via Op-Amp LH2011].
This reduces cable Capacitance, leakage and spurious voltages. Stability is increased with a small Capacitor connected at the input.
2: Wideband Unity Gain Inverting Amplifier.
This one compensates for the normal 6dB loss on 75 ohm coax runs. The one pictured above in the posted image states 13dB amplification, which sounds like this type of Inverting Amp.
13dB would be lossed over 3 RF inputs [3 TV sets], run through a "4 way splitter", more if two "3 way splitters" were used.
Judging from the frequencies listed on that amp, it would be used on high frequency CATV [capable of Analog with compressed Digital services], but more likely for a DSB type system.
950 - 2050 MHz is the bandwith of my DSB feed, however, I have noticed some newer CATV with Compressed Digital feed had this bandwith listed on the receiver.
Scott " 35 " Thompson
Just Say NO To Green Eggs And Ham!