Functions: A Fundamental Conceopt in Calculus

The book begins with an introduction to relations, since functions are a special type of relation. Chapter 2 presents the formal definition of a function as a relation between sets—numerical or otherwise. This sets the stage for Chapter 3, which focuses specifically on real functions, defined between sets of real numbers. These functions form the cornerstone of Calculus.

Special attention is given to graphing real functions and interpreting graphs as a tool for understanding functional behavior. Chapter 4 explores two of the most used real functions in Calculus: linear and quadratic functions. Chapter 5 introduces transcendental functions and offers a brief overview of other real functions frequently encountered in applications. The final chapter covers arithmetic operations on real functions, domain determination, and includes examples drawn from economic contexts.
Students using this book should be familiar with the symbols and language of propositional logic, as well as having a basic understanding of set theory. Those without this background are encouraged to consult introductory texts on these topics before proceeding.

Each chapter includes a series of exercises designed to reinforce the material. Answers to these exercises are provided at the end of the respective chapters.