Activity Overview
Students investigate the graphs of functions of the form y = 1/(x - a). They will discover that the graph of such a function has a vertical asymptote at x = a, and a horizontal asymptote at y = 0. They will investigate the graphic and numeric consequences of such asymptotic behavior by observing a trace point on the graph move in response to various inputs for the independent variable.
Objectives
- Students will explore the relationship between rational functions and both vertical and horizontal asymptotes. They will examine these relationships graphically and algebraically.
- Students will be asked to create sliders on the handheld to help in their exploration and discussions.
- Students will try to make a connection with how to understand these topics in IB Mathematics courses and on their final assessments.
Vocabulary
- Sliders
- Vertical Asymptotes
- Input
- Output
- Horizontal Asymptotes
About the Lesson
Students will explore the relationship between rational functions and both vertical and horizontal asymptotes. They will examine these relationships graphically and algebraically.
*Note: This activity includes optional IB support, including the IB Questions download for students who are preparing for the IB Exam.