Real Functions: Graphs and Properties

This lecture covers the concept of real functions, focusing on their graphs and specific properties such as symmetry. It explains how to determine the image of a function and explores the notion of surjection. Through examples, it illustrates the process of completing the square and how to analyze the periodicity of functions like sin(x) and cos(x). The lecture also delves into vertical and horizontal translations of functions, providing insights into their graphical representations and transformations.