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An introduction to the U.S. government
When the Constitution of the United States was drafted, a federalist government was born. A federal government system is indicative of shared powers between the national and state governments. The powers are divided based on the Bill of Rights: the 10th amendment allows states to obtain any powers not explicitly granted to the federal government. The state and federal governments are modeled the same, with three distinct branches that have power over one another. Not one branch was made to be more powerful than the rest, as the executive, legislative, and judicial branches work to balance each other out and make sure the constitution is being upheld effectively. Three common examples of this include: the executive branch is able to veto any bills made by the legislation branch (i.e. Congress); the judicial branch (I.e. Supreme Court) can overturn laws made by the executive branch; the legislation branch can reject the executive branch's nominees and outst the president if necessary.
An Introduction to your State Government

The state government is granted all powers that are not explicitly given to the federal government. In the state constitution, powers are further granted to counties. State governments mirror the structure of federal governments with bicameral (two house) congress for a legislative branch, a governor and elected officials and administrators for an executive branch, and a Chief Justice at the head of an intricate court systems for the judicial branch. The powers of the state include infrastructure (building and maintaining roads), education (public schools are funded and operating), public health (enforcing restrictions to protects citizens), economic restrictions (setting rules for businesses), environmental health (policies pertaining to the environment).
An Introduction to your County Government
Operated by an appointed board and elected officials, the county government is responsible for making and enforcing localized laws that do not conflict with the state legislature. The board allocates funding and oversees county departments and programs. Being more local than the state, county governments act as a greater representation of the people it serves. Often, state governments will delegate functions of the state to the counties, as counties hold some legislative power. In terms of acting within this legislative power, the Board of Supervisors can act via a resolution, board order, or ordinance. A resolution typically regards future actions of the Board, while a board order is a direct message from the Board to county officials. An ordinance is a local law that does not interfere with the state's laws. The county oversees the administration of regulations set forth by the state and federal governments. This includes recording documents, elections, criminal justice, health, welfare and agricultural enforcement.
An introduction to your city government
LA city is a charter city, meaning that it derives power from the state but amasses power over smaller issues in its charter. The city charter is a voter-approved document that serves as a "local constitution" for the city Each city is governed by an elected city council that creates and enforces local laws (ordinances). The city council is then responsible for supervising the operations of the elected city government. At this level of government, there is a city governor who acts similarly to that of the state governor in appointing figures and officials. They are accompanied by a 15 member city council. The city council is responsible for creating laws that apply to the City of Los Angeles and the maintenance of a budget for all departments and agencies. There are 15 city council members who represent each of the 15 districts that make up LA City. Furthermore, there is the City Attorney and their office which draft local and sometimes state laws, oversee the legality of departments and commissions, examine contracts and ordinances, and interpret the city charter. Finally, there is the city controller, who is the chief accounting officer of the city. The main function of the city controller is to audit, and oversee effectiveness in different city departments.