Final answer:
The brain stem, situated below the cerebellum, is responsible for controlling reflexes as well as vital functions such as respiration, heart rate, and the sleep/wake cycle.
Step-by-step explanation:
The brain structure located inferior to the cerebellum that controls reflexes and plays a critical role in respiration, heart rate, blood pressure, and the wake/sleep cycle is known as the brain stem. This structure, which is the lowest part of the brain, connects the rest of the brain with the spinal cord and is responsible for many unconscious functions. The brain stem is divided into three main parts: the midbrain, the pons, and the medulla oblongata. It's involved in various autonomic functions and the relay of sensory and motor neurons, which allows for signal transmission between the brain and spinal cord. In particular, the medulla oblongata within the brain stem is key for regulating the cardiovascular and respiratory systems.