Final answer:
The nurse's priority in determining the patency of the AV graft in a patient with chronic kidney disease is to check for a bruit using a stethoscope.
Step-by-step explanation:
The nurse's priority in determining the patency of the AV graft in a patient with chronic kidney disease is to check for a bruit by listening over the right arm AV graft site with a stethoscope. A bruit is an abnormal sound caused by turbulent blood flow, and its presence suggests that the graft is functioning properly. Checking the range of motion of the right arm and shoulder (option A), observing for clubbing of the fingers (option B), and comparing radial pulses (option C) are important assessments, but they do not directly assess the patency of the graft.