Many students may have a hard time dealing with polynomial long division, and the GSP lab may take a while. This lesson may take more than one day.
Objectives:
To recognize rational functions.
To sketch the graph of a rational function.
Materials:
Graphing Calculator with overhead
Geometer's Sketchpad
Graph paper
Textbook
Procedure:
This lesson only deals with rational functions whose numerators and denominators are first-degree polynomials.
Discuss and define a rational function.
Display the graph of a rational function on the overhead and discuss hyperbola, center, and asymptotes.
Show the students how to sketch f(x) = 1/x + 2. Then have them sketch f(x) = 1/(x+1) + 2.
We want the rational functions to be in the form f(x) = a/(x-h) + k, so sometimes we must do polynomial long division. Example: f(x) = (2x + 1)/(x + 2).
Have the students do pg. 648 A, B, C, & D in class.
The GSP activity is similar to the one for the quadratic function. Click here for the worksheet. Click here for the actual GSP graph.
Classwork/Homework: pg. 649-650 # 7-35 odd, 37, & 38.