What This Document Is
This document is Chapter One for a Calculus I course (MATH 1206) at Fordham University. It introduces the foundational concept of a function – a rule assigning outputs to inputs – and explores key aspects of their definition, representation, and manipulation. It lays the groundwork for understanding more complex calculus topics by establishing a firm grasp on function notation, domains, and ranges.
Why This Document Matters
This chapter is essential for students beginning their study of calculus. A solid understanding of functions is *required* to succeed in subsequent topics like limits, derivatives, and integrals. It’s used at the very start of the course to establish a common language and conceptual base. Students will use these concepts throughout the entire semester and beyond, in other math and science courses.
Common Limitations or Challenges
This chapter provides the *building blocks* for working with functions, but it does not delve into advanced function types or applications. It focuses on the core definitions and basic manipulations. It won’t teach you how to *apply* calculus to solve problems, only how to *describe* the functions you’ll be applying it to. Further study and practice are needed to master these concepts.
What This Document Provides
This chapter includes:
* An explanation of function notation (f(x)).
* Definitions of domain and range.
* Methods for graphing piecewise-defined functions.
* Examples of finding the domain of various functions, including rational functions.
* An introduction to function composition.
* A review of linear functions, including slope and intercept forms.
* An overview of polynomial and power functions.
* An introduction to exponential functions and their properties.
This preview does *not* include detailed solutions to all practice problems, advanced graphing techniques, or applications of these functions to real-world scenarios. It provides the foundational definitions and examples to prepare you for further study.