What term represents the authority by which courts and judicial officers take cognizance of and decide cases?

The term that represents the authority by which courts and judicial officers take cognizance of and decide cases is "jurisdiction." Jurisdiction refers to the legal power or authority of a court to hear and make decisions on specific types of cases. This authority can be determined by various factors such as geographical area (territorial jurisdiction) or the nature of the case (subject matter jurisdiction).

Understanding jurisdiction is crucial because it outlines the boundaries within which a court can operate and ensure that cases are heard in the appropriate court. For example, a state court may have jurisdiction over cases involving state laws, while federal courts will have jurisdiction over cases that involve federal laws or constitutional issues.

Other options represent different legal concepts but do not relate to the authority to hear cases in the same way as jurisdiction does. Venue, for instance, refers to the specific location or court within the jurisdiction where a case is tried, while habeas corpus is a legal principle that protects against unlawful detention. The right to hear is more of a general phrase and not a formal legal term, which is why "jurisdiction" is the most accurate choice in this context.