Why is unemployment The Feds Responsibility?

Just recently, I realised that the Feds are responsible for keeping the inflation rate and the unemployment rate under control. The first thought that came into mind. Why is unemployment The Feds responsibility?

For those who have not heard of The Feds, The Federal Reserve System (also known as the Federal Reserve, and informally as The Fed) is the central banking system of the United States. Its duties today, according to Wikipedia and official Federal Reserve documentation, are to conduct the nation's monetary policy, supervise and regulate banking institutions, maintain the stability of the financial system and provide financial services to depository institutions, the U.S. government, and foreign official institutions.

The problem is what has the nation's monetary policy or financial institutions for that matter have to do with unemployment? Why are the Feds given the responsibility of keeping unemployment low? The government rightly should be responsible for the unemployment because there is no direct linkage of monetary or financial policies on unemployment rate.

There are many ways to keep the unemployment rate low and financial means is just one of those means (e.g. loaning of money cheaply to businesses). By throwing the responsibility of unemployment to the Feds, you're severely limiting your options on how to reduce the unemployment rate. Can the Feds subsidise the salaries of citizens and provide training grants to all like the Singapore government? Furthermore, don't you find that controlling inflation rate and loaning of money cheaply to businesses a contradiction?

I still don't understand what the central banking system has to do with unemployment. Doesn't make any sense to me at all.