Which of the following is a general duty of any game official?

In the context of basketball officiating, administering penalties is a fundamental responsibility of any game official. This duty involves recognizing infractions during the game, such as fouls or violations, and enforcing the appropriate penalties as outlined in the rules. When an official sees a rule being violated, it is essential for them to act decisively, ensuring fairness and maintaining the integrity of the game.

This responsibility is crucial for upholding the game's standards and ensuring that players adhere to the established rules. While officials may also have other duties, such as making decisions on less common or ambiguous scenarios, their primary role centers around enforcing rules and penalizing infractions to maintain order and sportsmanship in the game.

The other options, although related to the officiating context, do not encompass the core duties in the same way. For instance, making decisions on points not specifically covered by the rules might occur infrequently, and granting time-outs is typically a procedural responsibility rather than a core duty. Communicating with players about personal issues is outside the official's scope of responsibilities and could compromise the impartiality expected in officiating. Thus, administering penalties captures the essence of an official's role in the game.