Final answer:
The swallowing center is located in the hindbrain, which is responsible for initiating and controlling the swallowing reflex along with other autonomic functions.
Step-by-step explanation:
When diagramming the brain for an anatomy and physiology class, nursing students would place the swallowing center in the hindbrain. The hindbrain includes structures such as the medulla oblongata, which contains the swallowing reflex center responsible for initiating this crucial process. This brain region manages autonomic functions necessary for survival, which also includes respiration and heart rate control. Located at the base of the brain connecting to the spinal cord, the hindbrain plays a pivotal role in managing these essential functions.