Final answer:
The task indicative of a registered nurse's responsibilities for a client with asthma and depression is monitoring the patient's respiratory status and response to medications.
Step-by-step explanation:
The task applicable for the registered nurse for a client with asthma and depression admitted to the hospital would be c) Monitoring the client's respiratory status and response to medications. Registered nurses are trained to assess and monitor patients' medical conditions closely. They have the expertise to observe changes in a patient's respiratory function, particularly with a condition like asthma, which may require direct supervision of a registered nurse. Monitoring could involve using a nebulizer to assess air expulsion from the lungs or detecting changes to inform treatment adjustments. Nurses also interpret vital signs and can manage complex situations that may arise during care. Furthermore, the registered nurse can provide more specialized tasks such as managing and adjusting medication regimens based on the client's response, which is crucial for patients with chronic conditions like asthma.