Which part of the brain controls vital functions like respiration and heart rate?

The hindbrain is responsible for controlling vital functions such as respiration and heart rate, making it the correct answer. This section of the brain includes important structures such as the medulla oblongata and pons, which are crucial for autonomic functions. The medulla oblongata specifically regulates involuntary functions like breathing and heart rate, ensuring that these essential processes occur without conscious effort.

In contrast, the mid-brain primarily plays a role in processing sensory information and regulating movement, while the cerebellum is focused on coordination and balance, controlling fine motor skills rather than vital autonomic functions. The hypothalamus, on the other hand, is vital for controlling various homeostatic processes and regulating hormones, but it does not directly control respiration and heart rate as effectively as the hindbrain structures do. Therefore, the hindbrain stands out as the key area responsible for these life-sustaining functions.