Chapter 1 - Functions and Graphs
In this chapter you will being the study of functions that will continue throughout the course. You will learn how to visualize functions graphically using a graphing calculator, and how their properties can be described using the notation and terminology introduced in this chapter. A familiarity with the terminology introduced will be essential for success in later chapters as we explore functions in greater depth.
(Demana, Franklin D. "Chapter 1." Precalculus: Graphical, Numerical, Algebraic. 7th ed. Boston: Addison-Wesley, 2007. 70. Print.)
Lesson 1.1 - Modeling and Equation Solving
We will cover numerical, algebraic and graphical models, the zero factor property, problem solving, grapher failure and hidden behavior, and finally a short section about proofs.
Lesson 1.2 - Functions and Their Properties
This lesson will introduce the terminology and concepts used throughout the course.
Lesson 1.3 - Twelve Basic Functions
This lesson covers the twelve basic functions and teaches how to analyze functions graphically and algebraically. Knowing these twelve basic functions and their properties will help throughout this course and in Calculus.
Lesson 1.4 - Building Functions From Functions
This lesson covers compositions of functions and how domain and range are affected.
Lesson 1.5 - Parametric Relations and Inverses
You will learn how relations can be defined parametrically, and what inverse relations and inverse functions are.
Lesson 1.6 - Graphical Transformations
This lesson reviews the concepts of graphical transformations covered in Algebra 2 and adds some new transformations.
Lesson 1.7 - Modeling with Functions
This lesson refers back to the first lesson about modeling. It also shows the various types of regressions that can be used to develop functions based on data.