Final answer:
Hearing and deciding cases involving federal law is not a function of the executive branch; this is the role of the judicial branch.
Step-by-step explanation:
The function that is not performed by the executive branch is hearing and deciding cases involving federal law. This function is reserved for the judicial branch, more specifically, the Supreme Court and other federal courts.
The executive branch's roles include carrying out the laws of the United States, representing the United States to other countries, and making treaties with other countries, but the judiciary interprets the laws and adjudicates legal disputes. The executive branch may enforce laws and policies, negotiate with foreign leaders, and participate in international affairs, but the responsibility for adjudicating cases lies with the courts.