Final answer:
The nicotinic receptor is both ionotropic and cholinergic, making it the correct answer for a receptor type that is influenced by drugs affecting both divisions of the autonomic system.
Step-by-step explanation:
The type of receptor that is both ionotropic and cholinergic is the nicotinic receptor. This receptor is a ligand-gated cation channel which, upon binding to acetylcholine (ACh), allows the flow of ions through the cell membrane, thus influencing the cell's electrical potential. The nicotinic receptor is found in the neuromuscular junction (NMJ) as well as other synapses within the body.
While nicotinic receptors respond to nicotine, another class of cholinergic receptors known as muscarinic receptors respond to muscarine but not nicotine. Hence, for a receptor that is both ionotropic and cholinergic, the correct option is E) nicotinic, whereas muscarinic receptors are not ionotropic as they are G protein-coupled receptors.