Final answer:
The mandibular branch (V3) of the trigeminal nerve has both sensory and motor functions, distinguishing it from the purely sensory ophthalmic and maxillary branches.
Step-by-step explanation:
The branch of the trigeminal nerve that has a motor component is the mandibular branch (V3). The trigeminal nerve is the fifth cranial nerve and it is primarily responsible for somatosensation (sensory functions) of the face. While all three branches of the trigeminal nerve—the ophthalmic, maxillary, and mandibular—have sensory functions, it is the mandibular branch that also controls the muscles of mastication, thus including a motor component. The mandibular branch is therefore unique among the trigeminal nerve branches for its dual sensory and motor functions.