Final answer:
To investigate a suspected fracture of the left olecranon in a canine patient, the technician should take radiographs of the left elbow.
Step-by-step explanation:
When the veterinarian orders radiographs to investigate a suspected fracture of the left olecranon in a canine patient, the technician should radiograph the left elbow. The olecranon is the point of the elbow and is part of the ulna, which is one of the two long bones within the forearm, the other being the radius. Radiographs of the elbow area will enable the veterinarian to assess any damage to the olecranon and surrounding structures and determine the appropriate treatment.