The document defines and discusses the importance of production functions. It defines a production function as the relationship between inputs of productive services and the rate of output. Production functions are important because they (1) help estimate production levels for given inputs, (2) indicate how firms can substitute inputs without changing output, and (3) help firms select the lowest cost combination of inputs to achieve a desired output level. Production functions also explain relationships like variable proportions and returns to scale and show the maximum output achievable from chosen input quantities. They assume no changes in technology, use of best techniques, divisibility of inputs, and applicability to short or long run periods.