Which of the following is a service a dental hygienist may perform under close supervision?

The service that a dental hygienist may perform under close supervision is taking final impressions. In the context of dental hygiene practice, close supervision implies that the dental hygienist must perform the task under the direct oversight of a licensed dentist. Taking final impressions requires a higher level of skill and understanding of dental anatomy and materials, which is why it falls under the category of tasks needing close supervision. This ensures that the impressions are accurate and meet the necessary standards for restorations or prosthetic devices, as any error could significantly impact the outcome of dental treatments.

In contrast, other tasks such as giving fluoride treatments, providing oral health instructions, and polishing tooth surfaces are typically within the scope of practice for dental hygienists operating under general supervision or even independently, depending on state regulations. These tasks are considered more routine preventive measures that do not carry the same level of complexity and risk, allowing dental hygienists more autonomy in performing them.