What is the best way to explain the production function equation to AP macroeconomics students as it relates to GDP?

The most efficient way to explain the production function mechanism is by use of the relationship between demand and supply.

People work or invest intending to make an income, and also why work without getting any returns. Therefore, the first step is ensuring that the consumers or the purchasers of goods and services got cash to buy them. Implementation of this idea requires governments and financial institutions to intervene by inducing cash flow in the economy. This process occurs through banks giving out loans or dividends and increased government expenditure on infrastructures, education, among other programs.

That way, the consumers get money to purchase commodities (aggregate demand) while investor's gains the capital to cater for production cost. As a result, enterprises are in a position to increase production output to satisfy the demand in the market. The same way does much workmanship is in need. Therefore, the employment rate rises and many people become financially stable. Besides, aggregate demand continues to rise as average supply increases.