Final answer:
The vagus nerve does not typically exert sympathetic effects as it is part of the parasympathetic nervous system, which induces rest-and-digest responses. It could potentially modulate the sympathetic system indirectly through the hypothalamus.
Step-by-step explanation:
The vagus nerve is primarily associated with the parasympathetic nervous system, which is responsible for the 'rest-and-digest' responses in the body as opposed to the 'fight-or-flight' responses governed by the sympathetic nervous system. The vagus nerve contains preganglionic parasympathetic fibers that release acetylcholine (ACh) onto nicotinic receptors to excite postganglionic neurons in terminal ganglia, which then release ACh to bind to muscarinic receptors in target organs, inducing parasympathetic effects.
So, in answer to the student's question on how the vagus nerve exerts sympathetic effects, the correct response would be that it typically does not. The vagus nerve is mainly involved in parasympathetic functions. However, it can exert indirect effects on the sympathetic system, specifically through option b. 'Indirect modulation through the hypothalamus,' but not by directly stimulating sympathetic ganglia.