How does the DHCP server determine the originating subnet of the DHCP client? | Networking

 DHCP servers store ranges of addresses that can be assigned to hosts on individual subnets. When a DHCP client starts up and if the DHCP client is on the same subnet as the DHCP server, the DHCP server can identify the subnet from the interface on which the DHCP messages from the client were received.
  When the DHCP client is on different subnet as that of DHCP server, a DHCP relay agent on the DHCP client's subnet records the IP address of the interface on which the DHCP message from the DHCP client was received before forwarding the message to the DHCP server.