Real Functions: Definitions and Properties

This lecture covers the definitions and properties of real functions, including parity, periodicity, and piecewise definitions. It explains the conventions for defining functions and explores examples to illustrate these concepts. The lecture also discusses polynomial functions, symmetry, and injectivity criteria, emphasizing the importance of understanding the domain and formula definitions. Additionally, it delves into the concepts of monotonicity, symmetry with respect to zero, and periodic functions. The composition of functions is exemplified to demonstrate how different functions can interact and produce new functions.