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 = x^{3}, y2 = 3^{x}

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