Final answer:
The Supreme Court’s primary function regarding lower courts is to establish legal precedents that guide their decisions, ensuring a coherent and consistent application of law.
Step-by-step explanation:
With regard to the lower courts, the Supreme Court's most important function is establishing legal precedents that will guide their decisions. The Supreme Court is the highest court in the land with the main responsibility to interpret and apply the United States Constitution, meaning that its decisions set binding precedents for all other courts in the federal system. Decisions of the higher courts are binding on the lower courts, which ensures that the federal courts operate with logic and consistency.