Final answer:
The trigeminal nerve is the cranial nerve with multiple functions, involving cutaneous sensations of the face and control of the muscles used in chewing.
Step-by-step explanation:
The cranial nerve that is responsible for performing multiple functions is the trigeminal nerve. This nerve is responsible for cutaneous sensations of the face, and it also controls the muscles used in mastication (chewing). Besides these functions, three branches of the trigeminal nerve—the ophthalmic, maxillary, and mandibular—convey sensory information from various parts of the face to the brain and are involved in certain reflexes such as the corneal reflex and sneezing.