Final answer:
The medulla oblongata within the brain stem regulates heart rate, respiratory rate, and vasoconstriction through the cardiovascular center and controls these functions by the sympathetic and parasympathetic nervous systems.
Step-by-step explanation:
The part of the brain stem that regulates heart rate, respiratory rate, and vasoconstriction is the medulla oblongata. This brain stem region contains the cardiovascular center, which controls the smooth and cardiac muscle of the cardiovascular system through autonomic connections. The cardiovascular center responds to changes in blood pressure and receives descending inputs from the hypothalamus that can increase activity in the cardiovascular system in response to factors such as stress. This center operates via the sympathetic and parasympathetic nervous systems, sending signals through the cardiac accelerator nerves and the vasomotor nerves to modulate heart rate and blood vessel constriction.
Furthermore, the solitary nucleus also plays a significant role in cardiovascular function by receiving sensory input and regulating sympathetic tone. The nucleus ambiguus and the dorsal motor nucleus contribute to the parasympathetic control of the heart by decreasing heart rate through the vagus nerve.