Final answer:
The correct term for generalized purplish blotching observed on a terminally ill patient's skin is mottling; it indicates reduced blood flow and is common as patients near end of life.
Step-by-step explanation:
When a nurse observes a generalized purplish blotching of a terminally ill patient's skin during a morning assessment, the correct term to document this finding would be mottling.
This is a common occurrence in patients who are terminally ill and indicates reduced blood flow and potentially the patient nearing the end of life.
Mottling is characterized by a blotchy, reddish-purplish marbling of the skin, and it is typically seen in dependent areas of the body.