Activity Overview
In this activity, students study the asymptotic behavior of rational functions. They explore the two types of asymptotes and make generalizations as to when they do or do not occur.
Before the Activity
See the attached PDF file for detailed instructions for this activity
Print pages 31 - 39 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Enter the function and find factors of numerator and denominator
Express f(x) in factored form and record it in the space provided
Find and record the zeros of each factor
Find and record, the y-intercept of the function by evaluating it at 0
Use the limit command to determine the behavior of f(x) as x approaches each zero of the denominator
Investigate the y-value to the right (positive value) and left (negative value) of zero
Record the vertical asymptotes in the table
Use the limit command to determine the behavior of f(x) as x approaches both positive and negative infinity, and record the values
Find and write the horizontal asymptote
Sketch the graph (vertical and horizontal asymptotes) based on the information on the grid provided.
Confirm the graph by graphing the function on the calculator
After the Activity
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary