Adjust Your Screen & Understand the Keys

Turn on your machine; the ON key is at the bottom left of the keyboard. A new calculator or one whose batteries are run down needs to have the brightness adjusted.

• To darken --- Press the yellow key (labeled 2^nd) and depress the blue ­ arrow key
• To lighten --- Press the yellow key and depress the blue ¯ arrow key

The Home Screen & Menus

Our tour begins at the home screen. Press QUIT (2^nd state next to yellow button) to open the home screen. The home screen is where calculations are made. The calculations on the next page involve symbols stored in the MATH menus. Before we get started with these examples, take a look at the MATH menus: press the MATH key (left side, under the green key).

Top Math menu

The MATH commands are organized into the 4 subsets listed across the top of this screen: MATH, NUM, CPX, and PRB. The MATH submenu is highlighted so its items appear. It contains more commands than we see so the last item includes the ¯ symbol. Press the ¯ key to scroll down to see three more commands. Press the ® arrow key to open a new submenu.  

Sample Calculations

Make sure you start each calculation from the home screen.

• Evaluate (-3)^3: type (-3) using the negatives symbol (-), open the MATH menu, arrow down to the third option, and press ENTER.

• Write .3875 into a fraction: type .3875, open the Math menu, highlight the command Þ Frac, press ENTER.

• Clean the screen: press the CLEAR key.

MODE SCREEN

There's always the chance that someone has left your calculator in a strange operating state, so when you begin, check the mode screen, shown above.

Line 1 refers to how numbers are presented. There's no need to switch from NORMAL mode. It engages scientific mode for large numbers and small numbers, and engineering mode is like scientific mode:  

Line 2 refers to the number of digits used. FLOAT is the default mode; in it the calculator decides how many decimals to use in the display.  

Line 3 refers to angle measurements. In angle mode, sin(60) equals 1/2 but in radian mode it won't. In radian mode you can put in a degree symbol, e.g., sin(60° ).

Line 4 refers to the type of formulas one wants to graph/table:

SEQ --- u, v or w is a recursive function of n

Line 5 refers to how graphs appear: as points connected by segments or as points 

Graph & Table Basics

The top row of keys has the graphics and table options. Our tour continues with a demonstration of how to use them to solve the following problem:

We'll enter length L as a function of width w and use its graph and table to get the L corresponding to w=9. Since 2L+2w=25, L=(25-2w)/2. To use the TI-83 we'll have to rename the variables: w becomes x and L becomes y1, y2, y3, or anyone of the default function names.

3 steps create our graph of L versus w as illustrated in the screens that follow:

1. Open the Y= screen (left side, under the screen) and enter this formula as shown on the left. Use the "hot key" (right of green key) to type x; this is easier than typing the 2-key ALPHA sequence for the letter X.
2. Open the WINDOW screen (next to Y=) and put in the values shown below in the middle screen.
3. Open the GRAPH screen (right key) to obtain the line shown at the right. X is between 0 and 13 with tick marks every 2 units because of the first three inputs in the WINDOW screen. Y is between -1 and 13 with tick marks every 5 units.

To capture a couple of points from the line, open TRACE mode by pressing the TRACE key in the top row. This places a blinking cursor on the line, at horizontal midpoint. The left and right arrows move the cursor along the line. In this example, the cursor starts at (6.5,6) and these coordinates appear at the bottom of the screen.

It's hard to get the cursor on the point where x=9 because that point isn't at one of the light pixels used in making this graph. Many texts, in such cases, suggest that students adjust the window or zoom-in on the point. A less frustrating option used the CALC commands (2^nd state on the TRACE key):

1. Open the CALC menu, highlight VALUE (left screen below)
2. Press ENTER to get the graph and type 9 (middle screen).
3. Press ENTER to see the coordinate corresponding to x=9 (left screen).

Another way to get function values is to make a table. We start with AUTO mode:

1. Open the 2^nd state screen TBLSET (above WINDOW).
2. Change its settings to match the screen on the left below.
3. Open the TABLE screen (above GRAPH) to see the same table shown below.

In AUTO mode, a table is "scrollable": we see entries for smaller x values by depressing the up arrow and larger ones by depressing the down arrow. ASK mode allows more control. Once the mode is changed in TBLSET (left figure below), open the TABLE screen (middle) and type 9 to get Y1=3.5 (right).

Tables have more columns when more functions are active on the Y= screen.

The Equation Solver

The previous example was really just an exercise in solving the equation 2L+2w=25 when w=9. This we can do using the SOLVE option, and we can do this without changing the variable names:

1. Open the MATH menu and highlight the 10^th option, Solver
2. Press ENTER to open the Solver screen and then press the ­ arrow to open the equation screen.
3. Type the equation so that all the terms are on one side and then press ENTER. In this case 0=25-(2L+2w) works.
4. All the variables used in your equation appear listed and set equal to 0. You must specify values for all of them; the value assigned to the unknown is an "initial guess" for its value. In this case, enter w=9 and L=0 works fine.
5. Place the cursor on the unknown and press ALPHA ENTER. After a few seconds the TI-83 updates the unknown with its (true) approximate value.

In general, an equation may have multiple solutions. Your choice of an initial guess influences which solution the TI-83 produces. Another way to limit the search is to alter the last line; it specifies the interval in which you seek a solution.
More Graph & Table Features

One of the most frustrating aspects of producing a graph is choosing a window. The TI-83 helps by picking the vertical parameters (YMIN and YMAX) that fit an x-interval we select:

1. Enter your function(s).
2. Put the XMIN/XMAX values you wish to use in the WINDOW screen.
3. Open the ZOOM screen (top row) and select the ZOOMFIT option.

Suppose you wish to graph or make a table of a composition of functions. For example, one might wish to check whether x^2+4 is the same as f(x+2) for f(x)=x^2. Fortunately, the TI-83 "understands" functional notation so one can compare their graphs using this feature. Unfortunately, the TI-83 does not recognize the "word" Y1 as the function with this name. It requires that we use a command that is stored in the Y-VARS submenu from the VARS screen shown below:

The submenu VARS contains screen parameters and quantities that are computed "behind the scene". They are divided into the categories shown in the figure above, e.g. Window, and each option opens its own submenu. For example, selecting Window opens a list of screen parameters that includes Xmin and Xmax. The Statistics option opens a screen displaying the names of five lists and the contents of the XY list: single-variable statistics about the last data set (x,y) that was active. These VARS symbols are typically used in writing programs.

The Y-VARS submenu is also divided into categories shown in the left figure below. Its submenu FUNCTION (right figure) contains the symbols for the functions: Y1, Y2, etc. When typing an expression involving a function, open this screen to highlight and copy its name just as one copies a symbol like Ö into an expression.

The following steps creates the composite function f(x+2) for f(x)=x^2 and sets up the graphical comparison with the function x^2+4:

1. Open the Y= screen, clear the Y1 and Y2 lines, and type in the formula X^2 as Y1.
2. Deactivate this curve (we won't want its graph confusing our comparison) by placing the cursor on its = and pressing ENTER.
3. Move the cursor to the Y2 line.
4. Open the VARS menu, arrow over to Y-VARS, and open the FUNCTION menu.
5. Highlight Y1 and press ENTER. This places the symbol Y1 on the Y2 line.
6. Type the rest of the composition expression as shown in the figure below.

7. Move the cursor to the Y3 line and type the formula X^2 + 4.
8. 8. Open WINDOW and make your parameter selections.

Another TI-83 feature makes viewing two or more graphs easier. Open the Y= screen. At the left side of each line there's an icon that symbolizes how the curve will be drawn. Arrow left of the Y and the icon blinks: strike ENTER to see the next choice of seven possible choices. The figure at the top of the next page displays the ``shade under'' option.

Look again at the Y= screen. Notice that the = sign of the function you used is quite dark. This denotes an "activated" function. The next table or graph constructed will include all the activated functions from the list. The = symbol is like a light switch: it turns off and on in the same way. In this case, placing the cursor an = symbol and striking ENTER changes it from OFF to ON or ON to OFF.

Other CALC Options

Option 2 finds the zero of a function in an x-interval you select. Options 3 and 4 optimize a function over an x-interval you select. Option 5 finds the intersection of two graphed functions over an x-interval you select. Option 6 finds the slope at a point you select. Option 7 integrates under a function between endpoints you select.

Each option requires you to input one or more x-values. You may do this in two ways:

1. Type the x-value from the keyboard as we did to find a value OR
2. Trace the curve to a point with that x-coordinate. Press ENTER to input its value.

The TI-83 limits the number of matrices that can be stored in memory to 10. The symbols for these matrices consist of square brackets around a letter, A-J: [A], [B], etc. These symbols don't appear on the key board, and they can't be typed The MATRIX screen shows three submenus . Like the FUNCTION submenu of Y-VARS, the NAMES submenu contains the matrix symbols. Its second submenu MATH contains operations such as ref( which converts a matrix to its reduced echelon form and rref( which gives the row-reduced echelon form. For example, if there's a matrix called [A] in memory, then creating the expression ref([A]) on the home screen is the first step to finding its reduced echelon form.

The third submenu EDIT is similar to the STAT EDIT submenu: one creates the matrix here. The following steps illustrate using MATRIX EDIT to make a 2x2 matrix [B]:

1. Open the EDIT screen (shown below on the left).
2. Place the cursor on the second option [B] and press Enter.
3. The cursor is in position to type the dimension of [B]: type 2, press ENTER, type 2, and then press Enter again. Notice that a matrix with 4 entries appears below.
4. Place the appropriate entries into the matrix. You may arrow from position to position or press ENTER after each change. In the latter case, the cursor moves down each row, going to the next row after reaching the row's rightmost entry.

Working with Data

The TI-83 data lists resemble spreadsheet lists. Six list names are fixed in the memory, and their names appear on the key board: L1 is the 2^nd state of the 1 key, L2 is the 2^nd state of the 2 key, etc. To restore your spreadsheet display to show L1-L6, open the STAT screen, highlight the 5^th option SetUpEditor and press ENTER.

There are 2 common data entry procedures: (1) enter the values one by one or (2) to download them from another calculator. The following steps create two lists L1 and L2 from the four data pairs (1,20), (2,37), (3,71) and (4,139).

1. Open the STAT menu (left figure below).
2. Select the Edit option to open the spreadsheet.
3. Clear the lists L1 and L2. To clear a list, place the cursor its name, press the CLEAR key, and then press ENTER.
4. Enter the four values in each list as shown below at the right.

STAT menu and the spreadsheet screen

The TI-83 was designed for statistics applications, and it has commands that none of the other TI calculators have. Those commands are in the STAT submenu TESTS. The CALC submenu contains many options for curve fitting. To plot data points (and the fitting curves) we use the STAT PLOTS menu (2^nd state on Y=).

The following steps produce a plot of the data you just entered:

1. Do some "housekeeping": check that you're in FUNC mode and deactivate all of the functions on the Y= list.
2. Open the STAT PLOTS screen (2^nd state of Y=), highlight a plot window, say Plot1, and press ENTER to open that screen.
3. Use the arrow keys to scroll down the screen and make the choices indicated in the middle screen below. This will produce a scatterplot of (unconnected) data points with L1 data on the horizontal axis, L2 data on the vertical.
4. To set the window so that the data points ``fit perfectly'', open the ZOOM screen (middle of the top row) and select option 9: ZOOMSTAT. Zoom options automatically create the graph.

The last stop on out tour will be the TI-83 regression or curve-fitting options. The data just entered will be our data, and since its graph seems parabolic we'll try a QUADRATIC fit (y=ax^2+bx+c). The formula will be computed and placed in y6.

1. CLEAR the homescreen, and open the Y= screen to clear the formula for Y6.
2. Return to the homescreen.
3. Press STAT and the arrow over to the CALC submenu.
4. Highlight the 5th option QuadReg and press ENTER.
5. Create the expression

QuadReg L1, L2, Y6

with the following steps: press L1 (2^nd on 1 key), press the comma (2^nd on 7 key), press L2 key, press the comma, and then paste the Y1 symbol from the Y-VARS submenu by opening the VARS menu, arrowing over to Y-VARS, selecting the FUNCTION option, and then selecting Y6.

6. Press ENTER and you'll see the regression formula. Press GRAPH to see its graph.

Regression result and plotted with data

Linking is a great way to share data sets with your students. Using the linking cables, you and your students can transfer lists in just a few minutes. To link, start by connecting 2 calculators, plugging each end of a linking chord into the circular opening at the front edge.

PRESS FIRMLY. Virtually all linking failure result from poorly connected cables.

The person receiving data has less to do:

1. Open the STAT submenu EDIT and clear the lists about to be received.
2. Open the LINK menu (2^nd on the variable key) shown below on the left.
3. Arrow over to RECEIVE, press ENTER and wait (screen is below on the right).

Sending a list is almost as easy. The following screens show the steps to send the contents of L3 and L4. We start by opening the LINK screen and then selecting the List option. This opens a screen with a list of the sender's lists in memory.

In the middle screen L3 and L4 have been activated for transmission. To activate a list and leave a bullet marking the its active status, arrow down to it and press ENTER. To make the transfer, arrow over to TRANSMIT (at the top) to open the transmission window. Press ENTER when the receiving calculator is ready.

The middle screen above shows a list named JOE. The following steps will create such a list and display it as the 7^th list on the EDIT screen. (One can insert a new list between any two displayed in the EDIT screen.) Our list JOE will contain the square roots of the values in L2:

1. Open STAT and press ENTER to enter the EDIT spreadsheet.
2. Place the cursor on the top row and arrow to the right of L6. This opens a new list.
3. Type the name JOE using the ALPHA keys and then press ENTER.
4. With JOE highlighted, type Ö (L2), and press ENTER.

Use your own TI-86 and follow the instructions in each Do Now, read the comments between the Do Nows, and if you start exploring on your own, you may have to backtrack in order to follow the next Do Now instructions.

Adjust Your Screen & Understand the Keys

Do Now --- Turn on your machine and adjust the screen brightness. Note: The ON key is at the bottom left of the keyboard. A new calculator or one whose batteries are run down needs to have the brightness adjusted.

• To darken --- Press the yellow key (labeled 2^nd) and depress the gray ­ arrow key
• To lighten --- Press the yellow key and depress the gray ¯ arrow key

The TI-86, permits "common" operations like ln, sin, and tan to be entered letter-by-letter, in either uppercase (ALPHA mode) or lowercase letters (alpha mode). To engage an ALPHA state on a key, press the blue key first. To lock the calculator in ALPHA mode (to type more than one letter consecutively), press ALPHA twice. To cancel ALPHA mode, press ALPHA again. Lowercase alpha is activated by the 2^nd state on the ALPHA key. Lock into lowercase alpha by first pressing the 3-key sequence 2^nd ALPHA ALPHA.

The Home Screen & Menus

Our tour begins at the home screen. This is where calculations are made.

Do Now -- Press QUIT (2^nd state next to yellow button) to open the home screen. Press the CLEAR key once or twice to erase everything on this screen.

Do Now --- Compute log (10^4) in two ways: (1) use the log key to create the expression thenpress ENTER to get the value (4); (2) lock into ALPHA mode to type the word log letter by letter, cancel ALPHA mode, finish typing the expression log (10^4), then press ENTER. The ^ symbol is above the division key ¸ . Most commands are not on the TI-86 keys; they are accessed through menus. The figure below shows the first page of the MATH menu line. It runs across the bottom of the homescreen. The arrow ® after MISC indicates that there is more to see on the menu list. The MORE key pages through menu lists, wrapping back to the start from the last page.

The MATH menu line: 1^st page

Do Now --- Open the second page of the MATH menu line: press the MATH key (2^nd state on times key X) to get the first page, and then press the MORE key (next to arrow keys) to move to the second page.

Do Now --- Open the MISC submenu: press MORE to return to page 1 of the MATH menu,press F5 because MISC is menu item displayed just above the F5 key. Note: with each menu the F-keys change. Each F-key turns on or opens the menu item displayed on the screen above it. Press the MORE key to display the second page of MISC items.

The 1^st page of the MISC line menu

Any time you select a menu item that displays another menu, the first menu line moves up to make room for the second. The item selected from the top line displays as black on white. The MORE key pages through the bottom menu line, and the F-keys (just under the screen) access its items.

The following Do Nows walk you through two calculations using commands copied from menus. The description of the second calculation is less detailed but involves almost the same steps as the first. Good luck.

Do Now --- Create the expression .3875Þ Frac on the home screen using the steps that follow. Once that's done, you can press ENTER to obtain the fraction equal to .3875, 31/80.

Start on the homescreen (press QUIT) and type .3875. Now you need to copy the command Þ Frac from the menu where it's stored. Since it's in the MISC submenu of the MATH menu, press the MATH key (2^nd state on the times key), locate the MISC option on the line menu, and press the corresponding F-key, F5 in this case. This choice opened a second line menu at the bottom of the screen. Look for the command Þ Frac on this bottom line menu. It isn't on the first page of options so press MORE to see the second page. Since it's now the first displayed option, press F1.

Look at the screen above the menu lines. You should see the expression we set out to create: .3875Þ Frac . Now you can press ENTER to finish the conversion to a fraction.

Do Now --- On the home screen, type the expression

Do Now --- Close all menus.
 

The CATLG-VARS Menus

The contents of all the TI-86 menus are displayed on pages 380-392 of the Guidebook that came with your calculator. However, there's an easier way to find things: the catalogue and the variables menus. All the stored commands, symbols and (temporary) variable values are found on the CATLG-VARS menu.

The CATLG submenu of CATLG-VARS displays all the TI functions and instructions in alphanumeric order; commands that don't begin with a letter are listed after the z. You can scroll through the list with the arrow keys ­ and ¯ . To speed up the process, type the first letter in the command name to move closer and then scroll. Note: when you enter the catalogue, the TI-86 goes into ALPHA mode anticipating that you'll want to type a letter.

Do Now --- Create the factorial expression 10! on the home screen and press ENTER tocompute its value, 3,628,8000. To do this, return to the home screen and type 10. To find the factorial symbol to put after 10, use to the catalogue. That is, press the CATLG-VARS key, open the CATLG menu, find and highlight the factorial symbol (!) and press ENTER.
 

MODE SCREEN

There's always the chance that someone has left your calculator in a strange operating state, so when you begin, check the MODE screen (2^nd state on the MORE key).

Do Now --- Open the MODE screen and check that all options match the defaults shown below. To make a change, use the arrow keys to highlight a new choice and press ENTER.

Line 1 refers to how numbers are presented. NORMAL is a good choice: it engages scientific mode for large numbers and small numbers. Engineering mode is like scientific mode:

Line 2 refers to the number of digits used. FLOAT is the default mode; in it the calculator decides how many decimals to use in the display:

Line 3 refers to angle measurements. In angle mode, sin (60) equals 1/2 but in radian mode it won't. In radian mode you may put in a degree symbol if needed, e.g., sin (60° ).

Line 4 refers to type of coordinates to use on your graphs: rectangular coordinates or polar coordinates.

Line 5 refers to the type of formulas one wants to graph/table:

  Graph & Table Basics

The GRAPH menu line has the graphics options, and the TABLE menu line has the table options. Our tour continues with a demonstration of how to use them to solve the following problem:

We'll enter length L as a function of width w and use its graph and table to get the L corresponding to w=9. Since 2L+2w=25, L=(25-2w)/2. We'll have to rename the variables: w becomes x and L becomes y1, y2, y3, or any one of the default function names.

Do Now --- Press GRAPH (below ALPHA key) and open the y(x) = screen ( F1). Press the CLEAR key to erase any previous formula and then type the formula (25-2x)/2 in the first line so it becomes the function y1. Note: y(x)= opens a second menu line containing an x: use this x instead of the ALPHA x. Look at the top row of this screen. If any of the words PLOT1, PLOT2 or PLOT3 appears in boldface, someone has left a data plot on. It must be turned off or it will interfere with our tracing: arrow the cursor up to its name and press SELCT (F5).

Do Now --- Open the WINDOW screen from the top menu line (M2). Use the arrow keys to put in the values shown in the WINDOW screen below. Note: The bottom menu line closed because you're no longer typing formulas.

Do Now --- Open the GRAPH screen (F5) and press CLEAR to remove the menu line and uncover the x-axis. Note: Because of the first three WINDOW inputs, the graph shows X between 0 and 13 with tick marks every 2 units. Y is between -1 and 13 with ticks every 5 units.

The point of having this graph was to capture points from it, including the pair with x=9.

Do Now --- Press the GRAPH key to bring back the Graph menu line and select the TRACE Option (F4). This places a blinking cursor on the graph at the horizontal midpoint, (6.5,6) in this case. Depress the right arrow ® to move the cursor close to the horizontal position x=9. The left arrow ¬ moves it backwards.

You can't place the cursor on the point exactly where x=9 because that point isn't at one of the light pixels used in making this graph. Many texts, in such cases, suggest that we adjust the window or zoom-in on the point. A less frustrating option when the x-value is within the dimensions of the displayed window is to type it from the keyboard while in trace mode.

Do Now --- Select the TRACE option, type 9, and press ENTER. The tracing cursor moves to the position where x=9 and the y-value (3.5) is displayed at the bottom of the screen.

Another way to get function values is to make a table. Tables can be created in two modes; we start with AUTO mode.

Do Now --- Press the TABLE key and open the TBLST (table set) editor (F2). Change the settings to match the TBLST screen below and then select TABLE to open the table screen. Note: To get the correct setting on the last line of TBLST, highlight AUTO and then press ENTER.

In AUTO mode, a table is "scrollable": we see entries for smaller x values by depressing the up arrow and larger ones by depressing the down arrow. ASK table mode allows more control.

Do Now --- Press F1 and adjust the TBLST to the options shown below. Note: remember to press ENTER after you highlight ASK. Now open the TABLE (shown in middle screen below). Type 9 in the x-column. Press ENTER to get Y1=3.5.

The Equation Solver

The fencing example started on page 5 is really about solving the equation 2L+2w=25 when w=9. This we can do using the SOLVER, and we can do it without changing the variable names:

Do Now --- Press the SOLVER key (2^nd state on GRAPH) to open the equation-entry editor.Press CLEAR to erase any previous equation. Type the equation, in this case 25=2L+2w. Note: Use ALPHA for L,w, and the = symbol (ALPHA state on the key above ON).

Press ENTER to open the interactive-solver editor where all the variables in your equation are listed. Enter a value for each letter except the unknown variable, and move the cursor to the unknown's line. In this case, make w=9 and place the cursor behind the L. Note: some variables may already have assigned values because these letters were used in some earlier calculation. Select the SOLVE option to engage the TI-86's numerical solver. The TI-86 updates the unknown value when it's done solving. In this case, L becomes 3.5.

In general, an equation may have multiple solutions. Your choice of the endpoints on the last line of the interactive-solver screen can be changed to pinpoint the interval in which you want the calculator to solve. The default endpoints (-1E 99 and 1E 99) describe an enormous interval.

More Graph & Table Features

One of the most frustrating aspects of producing a graph is choosing a window. The TI-86 helps by picking the vertical parameters (YMIN and YMAX) that fit an x-interval we select. In general, one first enters the function(s) on the y(x)= screen and the Xmin/Xmax values in the WINDOW screen. Since you have these entered already, go directly to the ZOOM menu to engage ZFIT:

Do Now --- Press GRAPH and select ZOOM. ZFIT is on the 2^nd page of the ZOOM line menu options, so use MORE find ZFIT. Select this option and the TI-86 makes a graph whose Ymin/Ymax values make the graph fit the screen with no extra space above or below.

Another TI-86 feature makes viewing two or more graphs easier: different curves can be drawn in different ways with dashes or heavy lines, etc.

Do Now --- Return to the y(x)= screen. In front of each formula there's an icon that symbolizes how its graph will be drawn. The icon is controlled by the STYLE option on the 2^nd page of the y(x)= menu. Each time you select STYLE the icon will change. Note: there are seven possible styles, including thin, thick and dashed lines.

Suppose you wish to store a function on the y(x)= list but you don't want it displayed in the next graph. Deactivate it. A formula is deactivated with the SELCT command on the y(x)=menu:

Do Now - Return to the y(x)= screen and deactivate y1: with the blinking cursor on the y1 line, press SELCT. Note: SELCT changed the = symbol's appearance. Press SELCT again to see the = in a black box, denoting an active state. Press SELCT again to deactivate.

Suppose you wish to check a composition formula graphically. The following steps create the composite function f(x+2) for f(x)=x^2 and set up the graphical comparison with x^2+4 :

Do Now --- Return to the y(x)= screen . If y2 already exists, place the cursor on its formula,Press CLEAR, and then type x^2 as its (new) formula. If y1 is the only function displayed, then press ENTER to create y2 and type x^2 as its formula. Deactivate y1 and y2. Now create y3, using the y from the bottom menu to type its formula as y2(x+2). Note: y3 is the composite expression f(x+2) and f is y2.

Create the y4 line and type x^2+4 as its formula. Change the STYLE icon on y4 and then select GRAPH to see y3 and y4, the only activated functions. Note: since their graphs don't coincide, f(x+2) isn't the same (algebraically) as x^2+4.
 
 

Making Data Lists

The TI-86 data lists resemble spreadsheet lists. Three list names are fixed in the memory: xStat, yStat and fStat. To restore your spreadsheet display to show them, use the command SetLEdit:

Do Now --- Return to the homescreen and CLEAR it. Select the command SetLEdit from the catalogue and press ENTER. The TI-86 responds with the word Done to indicate that the list editor screen is in default state. Press STAT (2^nd on the + key) and then EDIT to open the list editor. Note: depending on whether your lists have been used before, they may contain values.

The STAT EDIT screen

There are 2 common data entry procedures: (1) enter the values one by one or (2) download them from another calculator. The following steps create two lists xStat and another named MYOWN from the four data pairs (1,20), (2,37), (3,71) and (4,139).

Do Now --- Clear the list xStat: place the cursor on its name, press the CLEAR key, and then press ENTER. Create the new list by placing the cursor on the names line and arrowing past fStat: this opens a blank list and locks the TI-86 in ALPHA mode. Type the word MYOWN, press ENTER, and then using the arrow keys, enter the four values in each list as shown below.

The xStat & MYOWN lists

Using the linking cables, you can transfer lists (or anything else) in just a few seconds.

Do Now --- Connect 2 calculators, plugging each end of a linking chord into the circular opening at the front edge of one of the two. PRESS FIRMLY.

Decide which is the receiver and which is the sender, and each follows the appropriate set of steps that follow.

Do Now --- The person receiving data has less to do: clear out the lists about to be tranferred (in case they're not empty), open the Link menu (below EXIT) and select RECV. The TI-86 responds with the message that it's waiting.

The receiver does more when he/she didn't clear lists. In this case, a dialogue box will eventually appear offering options to overwrite, ignore (skip this transfer) or rename the transmitted list(s).
 

Sending a list is almost as easy. Start by opening the Link menu (below EXIT) and selecting SEND. This opens the SEND menu showing the categories of stored items. Press MORE to get the second page and select LIST from this page. A list with the names of all the sender's lists appears. Using the arrow keys, scroll to each list to be sent and press F2 to SELCT it. A bullet appears in front of each list selected.

To make the transfer, the sender selects the XMIT option on this same menu line.
 
 

Plotting Data Lists

The STAT menu line contains the CALC and PLOT submenus. CALC contains many options for curve fitting and PLOT deals with plotting data points. The following steps produce a scatterplot of the data you just entered. Before you make a data plot, it's a good idea to make sure other things are turned off and that the calculator is in the correct modes.

Do Now --- Check that you're in FUNC mode and deactivate all of the functions on the y(x)=list. Open the STAT menu, select PLOT (F3), and from its menu, select PLOT1. Note: The TI-86 can store set-up information for three different statistical plots called Plot1, Plot2 and Plot3. There are four lines of information to set-up PLOT1 as shown below. The first is set-up by moving the cursor to ON and pressing ENTER. Note: when the cursor moves to the second line, a new menu with different graph types open.

Press F1 to select SCAT from the type menu and press ENTER. Note: the Type menu closes and another menu with list names opens. The values selected for the Xlist are plotted along the horizontal axis and the data for Ylist is plotted on the vertical axis. Press F1 to select xStat for the Xlist Name, press ENTER, and select MYOWN for the Ylist Name and press ENTER.

The data points are marked by one of three symbols now showing on the newest bottom menu. The dots are barely visible so select either the squares or the circles.
  The final part of the data plotting process is shorter. We set up the WINDOW from the GRAPH menu:

Do Now --- Press the GRAPH key and select the ZOOM option. Use MORE to get to the second page and then select the ZDATA option. It works like the ZFIT you saw before, setting the window so that the data points ``fit perfectly''. Press CLEAR to remove the menu and see the x-axis. Curve Fitting to Data
 

The last stop on out tour will be the TI-86 curve-fitting options. The data in the lists xStat and MYOWN will be our data, and since its graph seems parabolic we'll try a 2^nd degree polynomial fit, P2Reg (y(x)=ax^2+bx+c). The following steps set up this fit, store the fitting formula as y5, and plot it and the data.

Do Now --- CLEAR the homescreen, and open the y(x)= screen to clear the formula for y5. Return to the homescreen because we'll create a fitting expression on the screen: open the STAT menu, select the CALC option, and then select P2Reg from the second page of its options. This puts the fit command on the homescreen. Finish typing the fitting expression: P2Reg xStat, MYOWN, y5. Note: You may type the names xStat, MYOWN, and y5 letter by letter or copy them from various the VARS submenus on the CATLG-VARS menu. The fitting expression consists of the fit type, followed by the Xlist name, the Ylist name, and the function name where the formula will be stored. Once it's been typed, press ENTER to obtain the result: (1) the coefficients are listed in alphabetic order shown on the homescreen below:

and (2) in this case, the formula 12.75x^2-24.65x+32.75 is stored as y5. To see the data and the fitting curve plotted together, open the GRAPH menu and select GRAPH.