Which piece of network equipment extends the cable range and allows connections to be made...

A repeater extends cable range by regenerating or amplifying a signal so it can travel farther without degrading. In Information Technology networking, signals weaken over distance due to attenuation and interference. A repeater receives the incoming signal, cleans or reconstructs it, and then retransmits it at full strength. This allows network segments to exceed the normal maximum cable length limits for a given standard and helps maintain reliable communication. Repeaters are commonly associated with the physical layer of networking because they deal with signal transmission rather than packet routing or traffic decisions. A switch operates mainly at the data link layer and forwards frames based on MAC addresses within a local network, but it does not primarily exist to boost signal strength. A router connects different networks and forwards packets using IP addressing and routing tables. A firewall is a security device that filters traffic based on rules to protect networks. Since the question focuses on increasing signal strength to extend range, the correct equipment is a repeater.