Which of the following is a type of delegated duty a dental hygienist may perform?

The correct answer is charting intra-oral and extra-oral conditions, as this task falls under the scope of practice for dental hygienists. Delegated duties are tasks that a dentist can assign to a dental hygienist, provided those tasks are within the hygienist’s training and the state's regulations governing practice. Charting is a fundamental duty that involves recording patients’ dental histories, findings from examinations, and other pertinent health information.

In comparison, providing legal documentation for practices is not typically a responsibility designated to dental hygienists, as this falls under the administrative and legal duties handled by dentists or practice managers. Directing dental surgery operations is well beyond the scope of a dental hygienist's training and authority, as it directly pertains to the provision of dental surgery, which is exclusively the responsibility of a licensed dentist. Lastly, prescribing medications to patients is a role reserved for licensed practitioners such as dentists or physicians, reflecting a level of authority and expertise that dental hygienists do not possess. Therefore, among the options provided, charting intra-oral and extra-oral conditions is the correct example of a delegated duty that dental hygienists may undertake.