Chapter 9 - Rational Functions
"This chapter presents opportunities for students to analyze, graph, and transform rational functions. The chapter begins with an analysis of key characteristics of rational functions and graphs. Lessons then expand on this knowledge for transformations of rational functions. Students will determine whether graphs of rational functions have vertical asymptotes, removable discontinuities, both, or neither, and then sketch graphs of rational functions detailing all holes and asymptotes. Finally, students will explore problem situations modeled by rational functions and answer questions related to each scenario."
"The ozone layer protects Earth from harmful ultraviolet radiation. Each year, this layer thins dramatically over the poles, creating ozone “holes” which have stretched as far as Australia and New Zealand." - Carnegie Textbook
Lesson 9.1 - Introduction to Rational Functions
"This lesson explores the graphs, tables, and values of rational functions including g(x)=1/x and r(x)=1/x^2 ." - Carnegie Textbook
Lesson 9.2 - Translating Rational Functions
"This lesson explores rational functions of the form g(x)=1/(x-c) for a constant value c." - Carnegie Textbook
Lesson 9.3 - Exploring Rational Functions Graphically
"This lesson provides opportunities for students to explore transformations of rational functions." - Carnegie Textbook
Lesson 9.4 - Graphical Discontinuities
"This lesson explores rational functions with graphical discontinuities." - Carnegie Textbook
End-Behavior Asymptotes and Graphing Rational Functions
This lesson is not in the text. In this lesson students will explore the characteristics of rational functions that are composed of polynomial functions that are not constants.
Lesson 9.5 - Using Rational Functions to Solve Problems
"This lesson provides opportunities for students to model problem situations using rational functions." - Carnegie Textbook