Which piece of network equipment extends the cable range and allows connections to be made by increasing the signal strength?

Routers are responsible for directing data packets between different networks and managing traffic within a local network. While they can connect multiple devices and manage data flow, they do not specifically enhance or extend the range of signals like repeaters do. Their primary function is to route traffic rather than amplify signals.

Switches operate at the data link layer and are used to connect devices within a local area network (LAN). They forward data packets to the correct device based on MAC address but do not amplify or extend the signal range. Their function is to manage traffic within a single network rather than extending connectivity.

Firewalls serve as security devices that monitor and control incoming and outgoing network traffic based on predetermined security rules. They are crucial for protecting networks from unauthorized access but do not have any capability to amplify or extend signal strength.