Final answer:
Network Address Translation (NAT) enables a gateway to rewrite the source IP of an outgoing datagram, allowing multiple devices to access the internet under a single public IP address.
Step-by-step explanation:
The functionality that allows a gateway to rewrite the source IP of an outgoing datagram is known as Network Address Translation (NAT). A gateway performs this task often because of the scarcity of IPV4 addresses and the need for maintaining multiple devices behind a single public IP. It involves modifying the network address information in the IP header of packets while they are in transit across a traffic routing device. This process allows multiple devices on a local network to be mapped to a single public IP address, enabling them to access internet resources.
NAT can be performed on various types of networks devices, but it is particularly associated with routers. The source IP is changed from a private, non-routable IP address to the router's public IP address. The router maintains a NAT table where it keeps track of each outgoing and incoming packet to match them correctly when the response from the internet comes back to the router.