## Section 17 for the TI-89

Some of these operations you should be familiar with on the TI-83 are listed below.

The graphing calculator has become an important tool in visualizing many of the ideas we study in mathematics class.  It is important that each student understands how to do basic operations associated with graphing, numerical analysis, and tables.  Some of these operations are listed below.

As a student continues their study of mathematics in an Advanced Placement Calculus class the graphing calculator will continue to help the student build a deeper understanding for the function numerically and graphically.  Once the student has developed these two foundational viewpoints the student will have less difficulty understanding the analytically study of the same mathematical concepts.

It doesn't matter which graphing calculator you use, all of the following skills are important on any graphing calculator.  These directions are specifically written for the TI-89 graphing calculator.

1. Working with the calculator in the correct mode

Graph Mode: (Function)

In most cases the student will want to make sure their calculator is in the Function mode.  Although there will be a few times when parametric, polar, and sequence mode will also be used.

Current Folder:

The TI-89 gives the students the option to store student-defined variables in different folders.  For most cases you will use the main folder.

Display Digits:

Students should round off all their final answers to THREE decimal places, but this means that throughout a problem a student should work with more than three decimal places (possibly five).  Then when the final answer is stated the answer should be rounded to THREE decimal places.

Angle Measurements:

Remember to always put your angle measurements in radians.  Many times you will have used your calculator in science class and put the angle measurements in degrees.

Most of the other settings you should leave at the default settings.  Remember if you happen to play some games on your calculators some of these default settings will be changed.  Remember to always return your calculator back to the default settings.

2.  Window dimensions:

The graphing calculator can graph a function in many different windows.  You can select minimum and maximum x- and y-values.  Most graphing calculators allow you to view a graph in a standard window {-10, 10, 1, -10, 10, 1}, but this is not necessary the best window to view all functions.  For example the function y=sin x would be better viewed in a window {-6.28, 6.28, 1, -1.5, 1.5, 1}.  Students should consider the behavior of a function and its range in building a window.

The TI-89 graphing calculator does have one zoom feature which makes building a window easy.  It is A:  ZoomFit.  You must first select a domain and then the calculator will determine what function values are needed to view the entire graph.  Suppose you had the equation and wanted to view it in the domain .  First enter the equation in a y-slot and set Xmin=0, Xmax=10, and Xscl=1. Press F2 Zoom and select A:  ZoomFit.

From the graph you can see that the function takes on many negative function values:  .  But it is not real clear what the function is doing about x=0.  To view the behavior around x=0 change Xmax=2 and re-build a window using ZoomFit.

This view shows the behavior the function between  .

3.     Table set and Table

To study a function numerically a student will often build a table.  To build a table automatically the student must tell the calculator the minimum value of x in the table and the increments between the x values.

Once these values are selected, and the student selects TABLE, the calculator can build an automatic table.

If a student wants to build a table with x values which are not equally spaced they may elect to build a table by ask mode.  When this mode is selected, and the student selects TABLE the student will input the x values and the calculator will determine the corresponding y-values for the selected x-values.

4.  Y= Key

When a student enters an equation in one of the function slots, the calculator will graph the equation in the selected window.   Very often a student forgets that an equation has been entered in one of the slots when working on a graph in a statistical mode.  These equations can be turned off so they don't graph at an inappropriate time.

5.    Stat Plots

From the Y= screen it is possible to tell if a statistical plot is turned on or off.  Always check the top of the screen to see if any of the STAT Plots are turned on before graphing an equation.  If they are turned on you can just clear them from the y= screen by highlighting them and pressing CLEAR.

You can access the data/matrix editor by pressing APPS and selecting 6.  Data/Matrix Editor.  At this point you can choose either to work on a current list, open a former list, or start a new list.

6.     Returning to the Home Screen

Students should know that 2nd Quit will always return them to the HOME screen for entering numerical calculations and commands.

7.    Entering numerical expressions

In most cases the graphing calculator usually follows the order of operations learned by most students as part of a pre-algebra course.  But there are a few exceptions.  Students should practice entering some of the following expressions to see whether they get the correct values. (Answer have been rounded off to three decimal places of accuracy.)

 Expression Answer -2 ~1.754 -32 ~.374 ~-0.180

Check Your Understanding:   Build an appropriate window to view each of the following graphs.  Be prepared to explain why you have selected each window.  In some questions a dot mode should be selected, while in other cases the connected mode should be selected.  The graph should show the behavior of the function for the given domain.

1. Graph the function for the real numbers -20 < x < 20.  After graphing the function in the given domain, find the value of y(100).

2. Graph the rational function for the real numbers -0.5 < x < 4.  After graphing the function in the given domain, find the value of y(4)-y(2).

3. Graph the function for the real numbers  1 < x < 10.  After graphing the function in the given domain, find the value of

4. First graph the function for the real numbers 1 < x < 5.  Then set up a table to find the values of  for the values x = 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3.