Final answer:
The glossopharyngeal nerve is responsible for motor impulses to the pharynx muscles and sensory impulses from the taste buds of the posterior one-third of the tongue, with the vagus nerve mediating the motor response of the gag reflex.
Step-by-step explanation:
The nerve responsible for sending motor impulses to the muscles of the pharynx and sensory impulses from the taste buds of the posterior one-third of the tongue is the glossopharyngeal nerve, also known as the ninth cranial nerve. It also plays a role in swallowing and the gag reflex, which involves the vagus nerve for the motor response of the reflex.
The facial nerve is associated with taste buds in the anterior third of the tongue, whereas the glossopharyngeal nerve serves the posterior two-thirds, and the vagus nerve connects to taste buds in the extreme posterior close to the pharynx.
The glossopharyngeal nerve relays general sensations from the pharyngeal walls and taste, which can trigger the gag reflex, mediated by the vagus nerve through contraction of the pharynx muscles, aiding in swallowing and speech functions. Proper testing for these functions involves stimulating the taste buds with various tastes and evoking the gag reflex using a tongue depressor.