Functions: Real Numbers and Graphs

This lecture introduces functions of real numbers, explaining how they associate each real number x with another real number f(x). Through examples, the instructor demonstrates the process of converting temperatures from Celsius to Fahrenheit using functions. The lecture also covers the concept of graphing functions, emphasizing the use of perpendicular and graduated axes to represent functions visually. Additionally, it explores the graph of an affine function of the form f(x) = a · x + b, showing that it results in a straight line. The presentation concludes with a proof that the points (0,0), (1,a), and (r,ar) are aligned on the graph of the function g(r) = ar.