# Activities

• • • ##### Subject Area

• Math: Math General: General

• ##### Author College

60 Minutes

• TI-86
• ##### Other Materials
This is Activity 2 from the EXPLORATIONS Book: Using the TI-86 in Collegiate Mathematics: A Tutorial

#### 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.

• 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