Functions using a Single Variable

In this chapter, we will delve into a variety of fundamental subjects related to the study of real functions and the transformations of such functions. To begin, we will investigate the absolute value, as well as the absolute value function, and examine the behavior and attributes of each of these concepts. Next, we will delve deeper into the world of functions, concentrating on the functions that are associated with a single variable and the graphical representations of these functions. As we move further, we will investigate the most important real-valued functions, such as polynomial functions and piecewise-defined functions, amongst others. Because of these functions, we are able to acquire a deeper comprehension of transformations and how they have an effect on function graphs. In this lesson, we will investigate the scaling and translating transformations, focusing on how they affect the features of functions. Examples and activities are presented throughout the chapter to help readers better understand the fundamental ideas behind graphical representation and function analysis.

Keywords: Absolute value, absolute value function, functions, functions of one variable, graph f , main real-valued functions, piecewise real functions, polynomial real functions, real-valued functions, scaling transformations, transformations, translation transformations.