Final answer:
Administering trimethaphan, an autonomic ganglionic blocker, to a patient typically results in vasodilation because it blocks both the sympathetic and parasympathetic systems, leading to a relaxed state of the blood vessels.
Step-by-step explanation:
When the anesthesiologist administers trimethaphan, which is classified as an autonomic ganglionic blocker, to an anesthetized patient, we would expect a response that is indicative of reduced autonomic activity. Such a drug would block transmission at the autonomic ganglia, affecting both sympathetic and parasympathetic systems. The most likely outcome of administering trimethaphan would be vasodilation because both the sympathetic system (which would normally promote vasoconstriction) and the parasympathetic system are blocked, leading to a dominance of the unopposed baseline state of the vessels, which is dilation. Other expected responses such as bradycardia could be mediated by the baroreceptor reflex as an indirect effect due to vasodilation and subsequent hypotension.