Final answer:
Medicare and Medicaid are federally funded health care coverage programs.
Step-by-step explanation:
Among the health care financing mechanisms mentioned, the federally funded options are Medicare and Medicaid.
Medicare provides health services to people over 65 years old and those who meet certain disability standards. It is funded by payroll taxes. Medicaid, on the other hand, provides services to people with very low incomes. It is funded by government tax dollars.