What of he following terms best describes the courts authority to hear cases before they have been appealed?

The term that best describes a court's authority to hear cases before they have been appealed is "original jurisdiction." This refers to the power of a court to hear a case for the first time, as opposed to appellate jurisdiction, which involves hearing cases that have already been decided by lower courts. Courts with original jurisdiction are typically the first to evaluate the evidence and make determinations in legal disputes.