Final answer:
The external domain of a cell-surface receptor is responsible for binding specific ligands, initiating cell signaling and communication.
Step-by-step explanation:
The function of the external domain of a cell-surface receptor is to bind to specific ligands, such as hormones, neurotransmitters, or growth factors, which leads to the transmission of a signal into the cell. This extracellular domain allows for the receptor to recognize and respond to external signals, facilitating cell communication and response to the environment. Depending on the receptor type, like enzyme-linked receptors, G-protein-linked receptors, or ion channel-linked receptors, the extracellular domain can vary greatly in size and function.