Nascent function concepts in Nova Scientia

The origin of the function concept is usually traced to Galileo's work on motion. We argue that specific proto-function concepts appeared in the work of Tartaglia a century before the publication of Galileo's Two New Sciences. The study of Tartaglia's ideas can be used in the classroom as a historical introduction to various function concepts, and certain modern extensions of Tartaglia's optimal range problem and inverse range problem are sources of enrichment for undergraduate courses in analysis, mathematical modeling and computation.