Final answer:
The function that begins after the observation of a gamma-ray burst is transmitted is alerting the Gamma-Ray Coordinates Network, which in turn informs ground-based observatories to look for the visible-light afterglow.
Step-by-step explanation:
When an orbiting high-energy telescope detects a gamma-ray burst, the Gamma-Ray Coordinates Network (GCN) at NASA's Goddard Space Flight Center is alerted. The network's function begins as soon as the observation is transmitted, with the primary goal to promptly inform ground-based observatories about the burst's rough location. This enables them to swiftly point their telescopes to the area in space to find and study the visible-light afterglow that follows the initial burst of gamma rays.
Astronomers rely on automated systems to promptly react to these gamma-ray bursts due to the need for speed in capturing the fleeting afterglows. These systems are in place to catch more bursts effectively and pinpoint their exact locations on a regular basis.