Final answer:
The agency that administers federal labor-management relations laws and investigates unfair labor practices is the National Labor Relations Board (NLRB), established by the Wagner Act of 1935.
Step-by-step explanation:
The federal government agency that administers the federal labor-management relations laws, investigates unfair labor practices, and settles labor disputes is the National Labor Relations Board (NLRB). The NLRB was established by the National Labor Relations Act of 1935, also known as the Wagner Act. This act aimed to protect workers' rights to unionize and bargain collectively, and mandated that employers recognize the legitimacy of a union if the majority of their workers were members. Notably, the Wagner Act and the NLRB played crucial roles in affirming the rights of workers and solidifying the government's commitment to supporting industrial workers during the New Deal era. Therefore, the correct answer to the student's question is option b: National Labor Relations Board.