Final answer:
The brainstem, specifically the medulla within it, contains the vasomotor and respiratory center, thus controlling vasotone, arterial pressure, heart activity, and breathing. The hypothalamus also plays a role in regulating homeostasis broadly via hormonal and autonomic functions. The correct answer is a) Brainstem.
Step-by-step explanation:
The part of the brain that has a vasomotor (which controls vasotone, arterial pressure, heart activity) and respiratory center (controls inspiration and expiration) is the brainstem. Specifically, within the brainstem, the medulla contains nuclei known as the cardiovascular center, which regulates the cardiovascular system via autonomic connections. This area of the brainstem is also responsible for regulating the respiratory system. The respiratory and cardiovascular control centers within the medulla respond to various stimuli, such as changes in blood pressure or carbon dioxide levels, thereby maintaining homeostasis in partnership with inputs from higher centers like the hypothalamus.
It's important to distinguish the brainstem's roles from that of the hypothalamus. The hypothalamus regulates homeostasis for many bodily functions but through systemic hormonal control and direct autonomic regulation rather than localized control of specific functions like vasomotor and respiratory activity which is a key role of the brainstem.
Therefore, the correct answer to this question is: a) Brainstem.