Rational Functions Calculation and Graphing Project

PLEASE NOTE: THE PREVIEW VERSION OF THIS PRODUCT IS THE ACTUAL "STUDENT VERSION" AND DOES NOT INCLUDE ANY OF THE ANSWERS TO THE PROBLEMS. THE PRODUCT VERSION INCLUDES DETAILED ANSWERS TO ALL OF THE PROBLEMS FOR THE PROJECT.

This project activity involves the calculation, graphing and coloring of basic rational functions/equations. I have my Algebra 2, Math 3 and Precalculus students complete this project toward the end of the unit on rational functions. As noted in the TpT "Preview" section of this product, please note that this project does not involve the review, calculation or graphing of higher level rational function concepts such as "hole" discontinuities or slant asymptotes.

A total of eight (8) functions are provided that require students to calculate the following for each one:

• Vertical and Horizontal Asymptotes
• Transformations (Vertical Stretch & Shrink, Reflectiion over the X-Axis and Horizontal and Vertical Translations
• Function Domain and Range
• X-Y Intercepts

A series of very organized calculation sheets are provided for the students to calculate the above information for each function. Once these calculations are complete, the students will list the results on the Rational Function Summary Table. This is followed by the completion of sixteen (16) "x-y" coordinate point tables by the students to facilitate their graphing of the 2 branches of each function. A minimum of four (4) "x-y" coordinate points are required for the graphing part of the project. These points are then plotted for each branch of the functions/equations and a smooth curve is to be drawn on the furnished graph grid for each function/equation. Finally the various sections formed by the intersecting lines of the plotted graphs are to be colored to provide an interesting "stained glass effect" final product.

This activity can be completed by students working individually; but, given the amount of calculations and graphing involved, I have my students work in pairs or groups to complete the project in a more timely manner. It usually takes two, 1-1/2 hour class periods to completely finish all parts of the activity with some of the final graph coloring also being assigned as homework.

This project activity package is an MS Word file and includes the following sections and appendices:

• Part A - General Introduction
• Part B - General Vocabulary
• Part C – General Rational Function Curve Characteristics
• Part D – Introduction to Asymptotes
• Part E – Domain and Range of Rational Functions or Equations
• Part F – Basic Steps to Solve Rational Functions or Equations
• Part G – Basic Steps to Graph Rational Functions or Equations
• Part H – Project Specific Guidelines
• Part I – Grading Rubric

• Appendix A - Student Worksheets including:
  • Rational Equations Calculation Sheets
  • Rational Function Summary Table
  • Rational Equation X-Y Coordinate Point Tables
  • Blank Appendix B Graph Grid

• Appendix B - Graph Grid
• Appendix C - Grading Rubric
• Appendix D - Teacher Answer Key Material including:
  • All completed calculation sheets with answers,
  • Completed Rational Function Summary Table,
  • Completed Rational Equation X-Y Coordinate Point Tables, and
  • Graphs (1 - uncolored and 2 - colored)

In addition two (2) completed, sample, colored graph grid examples are also included at the end of the activity package. There are 30 total pages in the package. The native MS Word file is included in the event the teacher desires to make any modifications to the activity to suit her or his classroom purposes.

Other MS PPT products for 6th Grade, 7th Grade, 8th Grade, Math 1, Math 2, Math 3, Algebra 1, Algebra 2, Geometry and PreCalculus curriculum topics can be reviewed and purchased under my TpT page titled: "Priceless Math".