Graphing Topics:

Function Plot F3 Trace F2 Zoom Window Multiple Plots

F5 Math Tool Bar Tables Trigonometric Graphs 3D Graphs

Graphing Mode

Let's start by plotting graphs of functions in the Cartesian Coordinate System. But before we begin, check to see if the calculator is in function mode by looking for a FUNC on the Status line.

If you do not see a FUNC, you will have to change the MODE to function. Press the key for the screen below.

Highlight FUNCTION and press the right arrow on the cursor pad.

There are five graphing mode options available on the TI-92 calculator including; FUNCTION, PARAMETRIC, POLAR, SEQUENCE AND 3D.

Highlight 1: FUNCTION and press ENTER then ENTER again. This will bring you back to the Home page in function mode.

If you press the MODE key and realize that you do not want to change any settings, just press the escape (ESC) to return to the Home screen. The escape key can be used to bring you back to a previous screen.

Function Plot

Before graphing a function, you must first type the function in the function editor. There are two methods to get to this screen. One method is to press the diamond key then the W (Y=). This will generate the screen below.

The other method is to press the APPS key which is located to the left of the cursor pad.

Then press 2 or use the cursor pad to scroll to the Y= Editor. You can use the APPS key to quickly change from on application to another. Note that if you scroll up there are two plot types, functions and data plots.

We will start by entering in a linear function with a slope of 2 and a y-intercept of 4.

Enter a 2x + 4 next to the y1(x) = and press ENTER. Note that you do not have to enter a multiplication sign between the 2 and the x. The equation should move to the history area of the function editor.

To plot a graph of this function, press the diamond key and R (GRAPH) or use the APPS key and go to 4: Graph. The graph should look like the diagram below.

F3 Trace

Note that when you are in the graph mode, the Toolbar on the top of the screen changes to graphing functions.

Press the cursor pad to move the cursor on the screen. To place the cursor directly on the function, press F3 for a Trace. The cursor should move directly on the function. Now when you move the cursor, it will move along the function. The coordinates of the cursor are shown on the bottom of the screen next to xc: and yc:. If you would like to move the cursor in increments of 10 pixels, press and hold down the 2nd key and then press the cursor key.

To move to a position on the graph for a specific x value, type in the value and press ENTER. If you choose a value for x that is off the screen, the cursor will disappear. Press ENTER for the graph to redraw about the cursor.

F2 Zoom

If you press F2 for Zoom, you will see the screen below.

The TI-92 calculator allows you to perform a number of zoom options. A few are listed below.

ZoomBox lets you draw a box and zoom in on that box.

ZoomIn and ZoomOut allows you to zoom in and out by an amount defined by SetFactors.

ZoomStd sets the Windows variables to their default values.

ZoomFit adjusts the viewing window to display the full range of dependent variables for the selected function.

SetFactors lets you set Zoom factors for ZoomIn and ZoomOut.

Let's first look at the ZoomIn option. Press 2: Zoomin. Place the cursor on the center of the zoom graph then press ENTER.

To get the graph back to the default setting, Press F2 then 6: ZoomStd.

Press F2 then A: ZoomFit and note how the graph changes to show all x values from -10 to +10.

Window View

To change the view of the graph, press the diamond key and E (WINDOW). The WINDOW screen enables you to change the window graph options max, min, scaling and the resolution.

Change the xmin to -2, xmax to 6, ymin to -2 and ymax to 25. Then press the diamond key and R (GRAPH) to graph the linear function. Note the new graph.

Multiple Function Graphs

You can graph more than one function on the same screen with the TI-92 calculator. Press the diamond key and W to go back to the function editor and enter the function y2(x) = x^2 by pressing x and the ^ key then 2. Press the diamond key then R (GRAPH) to view the both graphs simultaneously. Press F2 then 6: ZoomStd.

Press F2 Zoom and 1 for the ZoomBox. This function enables you to zoom in a specified box. The first step is to specify a corner of the box. Move the cursor to a corner and press ENTER. Then use the cursor pad to draw a box.

The coordinates of the opposite corner of the box are shown on the bottom of the screen. When the box is in the correct position, press ENTER. The calculator will redraw the graph specified by the box.

F5 Math

From the graph screen, select F5 Math.

The TI-92 calculator allows you to select a number of different math options. A few are listed below.

Zero finds a zero (x-intercept).

Minimum and Maximum find a minimum and maximum point within an interval.

Intersection finds the intersection of two functions.

Derivatives find the derivative (slope) of a point.

Inflection finds the inflection point of a curve.

Tangent draws a tangent line at a point and displays its equation.

Let's start by looking at the intersection of these two functions. Select 5: Intersection. Press ENTER for the first function and press ENTER again for the second function. If there are more than two functions graphed on the screen, use the cursor pad (up or down arrow) to select the two with which you want to find the intersection.

Next, move the cursor to the Lower Bound x value i.e. move the cursor to a point on either curve to the left of the intersection point.

Then specify the Upper Bound point by moving the cursor to the right of the intersection point. Lower and upper bounds are defined by the x values. Then press ENTER. The intersecting of the two functions will be show at the bottom of the screen.

Experiment with the other Math functions. Note that to evaluate options like minimums, maximums and definite integrals, lower and upper bounds will have to be specified.

Function Editor Toolbar

Go back to the function editor screen by pressing the diamond button then W (Y=).

Use the cursor pad to highlight the linear function y1 = 2x + 4. Press F6 Style then select 2: Dot.

Press the diamond key and R (GRAPH) to graph the functions. The linear function will now be graphed with dots.

This graphing option enables you to easily distinguish between various graphed function. Go back to the function editor screen.

Enter the function y3(x) = x³ under the x² function.

Now if we wanted to plot only the linear function y1 = 2x + 4 and the new function

y3 = x³ and not the function y2 = x² , we can either delete y2 or delete the check next to the function. To delete a check, highlight the function then press F4. The TI-92 calculator will only graph the checked functions. Next check the graphs of the functions.

Note that the y2(x) = x² function is not graphed.

Tables

The TI-91 calculator also has a table screen. To get to the table screen, press the diamond key and T (TABLE) or use the APPS key and go to 5: Table. You will see a table of values for the two functions.

The function TblSet lets you customize the table view.

Trigonometric Graphs

Go back to the function editor and define y1 = sin(x). Plot the function and zoom in to ZoomStd.

The function is hard to see. Change the mode to radians and regraph.

Go to WINDOW and change xmin to -2p, xmax to 2p ymin to -2 and ymax to 2. Then plot thegraph.

Next plot from -3p to 3p.

3D Graphs

Before plotting a 3D graph, you must first change the MODE setting. Press the MODE key and change the mode next to Graph...... from FUNCTION to 3D.

When you switch to the graphing editor Y=, you will be prompted for z1 as a function of the variables x and y. The z will be plotted on the vertical axis.

Enter the function z1(x,y)=x*y. You must insert a multiplication sign * between the variables x and y. Otherwise the calculator will interpret the expression xy as one variable.

Press the diamond key then R(GRAPH) to plot the three dimensional graph. It will take a few seconds to render a 3D graph.

Next press F2 Zoom then 6: ZoomStd to look at the standard view of the graph.

To change the graph format, press the diamond key then F.

Change the Axes and Labels and press ENTER to redraw the graph.

You can change the graph view by pressing the diamond key then E(WINDOW). This window gives you the option to change the max and min values for x and y and also the ability to rotate the 3D diagram.

Experiment by changing the max and min numbers and change eyeqº to 80 and graph the function.