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There are four steps in defining a graph in the TI-85, namely:
1. Set the Mode
2. Set the Format
3. Enter the Function to be graphed
4. View the graph
This chapter outlines how to define a graph and then proceeds to illustrate how the graph may be explored using the TI-85 graph features.
Press [2nd] [MORE] and the following screen appears:
The graphing modes available on the TI-85 are Function, Polar, Parametric and Differential Equation graphing. As we shall be graphing functions in this chapter, select [Func] which is on the fifth line of the display.
Press [GRAPH] [MORE] [ F3 ] to select the appropriate modes for the graph. There are seven choices to be made :
These choices are self-explanatory and are :
1. rectangular or polar graphing display
2. cursor co-ordinate on or off
3. drawline or drawdot graph display
4. sequential or simultaneous graphing
5. grid on or grid off
6. axes on or axes off display
7. axis label off or axis label on
On the TI-85, functions are graphed for x and y, where x is the independent variable and y = y(x). For example, graph the function y = x sin 2x:
The viewing rectangle is the rectangular portion of the co-ordinate plane determined by the user. The [-10,10] by [-10,10] viewing rectangle is called the standard viewing rectangle.
Press [GRAPH] [F2] to enter values for the viewing window of interest. Select [GRAPH] [F3] [F4] for the standard viewing window:
After creating and selecting the function to graph, and defining the appropriate viewing rectangle, we may now display the graph:
The graph can be explored a number of ways. Here we shall implement the zooming and tracing features of the TI-85.
The free moving cursor is engaged and moved by the arrow keys. To see the moving cursor press [GRAPH] and the arrow. The line above the menu shows the x and the y co-ordinate values for the cursor position (x,y). As the user moves the cursor, the x and y co-ordinate values are updated continually with the cursor position.
Using the TRACE feature of the TI-85, the user can move the cursor along a function, showing the x and y display co-ordinate values of the cursor location on the function:
The co-ordinate values of the cursor location (x, y1(x)) are displayed on the bottom line of the display - no menu items are shown. The y value is the calculated value of the function for the displayed value of x. In other words, if y1 = f(x), then the value of y shown is f(x).
] and [ 
] to move along the function
until you have traced the largest y-value for 0 < x < 5:
The viewing rectangle can be magnified around a specific cursor location by selecting [ZIN] from the [ZOOM] menu. To zoom in :
For example, zooming in on the point traced earlier provides:
Follow the same procedure for zooming out - [ F3 ].
When ‘zooming in’ a larger factor will increase magnification, whereas a smaller factor will decrease magnification. A corresponding result occurs for ‘zooming out’. To change the zoom factors we use [ZFACT]:
To create a specific viewing window use the zoom box feature:
The chosen viewing window should now be displayed. The screen below shows this feature being implemented:
Within the operations on the GRAPH MATH menu, you can analyse a displayed graph to determine where minimum and maximum values, inflection points and intercepts occur. To activate this menu:
1. Press [GRAPH] [MORE] [ F1 ], press [MORE] to display additional items on the GRAPH MATH menu:
To find a minimum graphically:
1. Press [ MORE] [F1] to select [FMIN].
The trace cursor appears near the middle of the screen on the function on the point (x, y1(x)).
2. Press [ENTER]
The calculator computed minimum is displayed in the cursor co-ordinates at the bottom of the display. This is the most accurate of the three graphical solutions, fmax, zoom, and trace, which have been discussed.
This brief chapter introduced you to some basic TI-85 graphing operations. You should consult the TI-85 User’s Guide to learn about these features in more detail. Other capabilities are outlined below and the TI-85 User’s Guide Chapter references are noted in parentheses:
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