dagM61_20250204_ave_rate_of_change__equation_of_constructed_recip_graph__composite_functions__48

AI synopsis: Dave discussed the concept of average rate of change, including its calculation and depiction on a graph. He also explored the idea of instantaneous rate of change, composite functions, and the importance of understanding notation and following the order of operations. Lastly, he touched on the restrictions on domain and range, patterns in mathematical functions, and the concept of functions and their domains.
He explained how to calculate the average rate of change using the function notation and the definition of average rate of change. He also demonstrated how to depict the average rate on a graph, emphasizing the importance of understanding the concept for future calculus courses. David also clarified the difference between the rise, run and slope in the context of the average rate of change.
The discussion then moved to the notation and concept of composite functions.