Final answer:
The vagus nerve is the component of the parasympathetic nervous system that controls digestive functions and is responsible for promoting rest-and-digest responses.
Step-by-step explanation:
The parasympathetic nervous system controls digestive functions and alters the activity of the digestive system via the vagus nerve. The vagus nerve is responsible for a variety of tasks including controlling the muscles that result in the gag reflex. The vagus nerve contains preganglionic parasympathetic fibers which are involved in promoting rest-and-digest functions, such as decreased heart rate and increased digestion ability.