Final answer:
The trigeminal nerve (cranial nerve V) innervates the muscles of mastication as well as providing sensory input from the face, including the teeth, gums, and lips. The facial nerve and vagus nerve are responsible for facial expressions and the gag reflex, respectively.
Step-by-step explanation:
The cranial nerve responsible for innervating the muscles of mastication and providing sensory impulses from teeth, gums, and lips is the trigeminal nerve (cranial nerve V). This nerve also tests for stretch reflexes associated with chewing.
The facial nerve (cranial nerve VII) is responsible for motor functions like facial expressions, which can be tested by having the patient make various facial movements including raising eyebrows, smiling, and frowning. The vagus nerve (cranial nerve X) is involved in the motor control of the gag reflex, which is a test of its function, and contributes to the regulation of the heartbeat and digestion due to its parasympathetic functions.