Final answer:
The function in ultrasound systems that compensates for the reduction in intensity of the sound beam as it travels through tissue, due to attenuation, is Time Gain Compensation (TGC).
Step-by-step explanation:
The ultrasound system function that enables the sonographer to adapt to the amount of attenuation that occurs with increasing depth is Time Gain Compensation (TGC).
Attenuation in ultrasound refers to the reduction in intensity of the sound beam as it travels through tissue. The TGC function allows the user to adjust the amplification of the received echoes at different depths to compensate for this loss of signal strength. It helps to create a more uniform image by making deeper echoes appear brighter, which would otherwise be weaker due to attenuation.
The options provided were focusing, receiver gain, TGC, and output power. While all the functions are important in the use of ultrasound systems, it is TGC that specifically addresses the issue of adapting for the depth-related attenuation.