Education Technology

Advanced Graphing and the GRAPH MATH Menu

Activity Overview

In this activity, students use the graphing capabilities of the TI-86 to graph different functions. They develop capabilities for analyzing a graph using several of the items contained in the GRAPH MATH menu.

Before the Activity

  • Set up the calculator as explained in the activity
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 23 - 38 from the attached activity PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Use the ROOT option to find the zeros of a polynomial function
  • Enter the values for the left and right bounds

  • Enter the polynomial function and two absolute value functions and graph them
  • Find the points of intersection between the vertical lines given by bound values

  • Graph a polynomial function, enter the bound values, and select the Fmin option to get the local minimum value
  • Understand that Fmin and Fmax options are sensitive to the value of Guess as to which local minimum or local maximum they locate

  • Access the Catalog/Variables menu to type names of instructions, functions, or variables

  • Graph functions y1 = x3, y2 = 3x
  • Observe the points of intersection
  • Use the table feature to see the numerical evidence of the intersection
  • Graph the function y3 = y1 ? y2, and observe the range where its roots lie
  • Equate the functions y1 and y2, and use the ROOT option to find the first root

  • Enter a piecewise function
  • Select an appropriate graph style to get a more accurate version of the graph
  • Recognize the fact that if the function has a complex form, the TI-86 will not plot the point (x, f(x)) even if the imaginary part is zero

  • Use the Zoom Box feature to determine if two graphs intersect in the first quadrant

  • Enter a rational function and set the window settings
  • Observe that the calculator plots points for an x-value to the left and right of the asymptote, and connects the points with a line segment which appears nearly vertical
  • Verify this by changing the graph style
  • After the Activity

    Students complete the exercises on the Activity sheet.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary