Real Functions: Definitions and Graphs

This lecture introduces real functions, starting with definitions and terminology to establish a common foundation. The instructor explains the concept of a real function as a relation F that maps elements from a domain A to images in R. Key definitions such as domain of definition and image of F are discussed, along with the concept of a function's graph. Examples are provided to illustrate functions like square root of X + 1 and the floor function. The lecture also covers the notions of parity, periodicity, and monotonicity, emphasizing the geometric interpretation of these properties. The instructor concludes by exploring the concepts of boundedness and absolute value functions, highlighting their significance in understanding limits and improper integrals.