Which of the following statements is true about special districts?

Special districts are indeed primarily established for single-purpose functions, which makes this statement true. These districts are designed to focus on a specific service or function, such as water supply, sanitation, public transportation, or education, and they operate independently of other levels of government to fulfill these specific needs. This specialization allows for more efficient management and provision of services tailored to the needs of the community they serve.

In terms of the other statements, the assertion that special districts have authority over several counties is misleading, as their jurisdiction can vary widely and is often confined to a specific area, not necessarily encompassing multiple counties. The claim about operating without funding restrictions does not hold, as special districts typically have to adhere to specific funding guidelines and regulations, which govern how they can raise and allocate funds. Lastly, the suggestion that they manage state services throughout Texas overlooks that their creation and operation are localized, primarily focused on specific community needs rather than statewide service management.