Calculator Notes (TI-86)

Absolute Value on the TI-86 (TI-85).  2nd    CUSTOM    f1(catalog)     (then get the arrow beside abs ---use ALPHA  A to get to the a's in the list)  ENTER  Be sure to put expression for which you want to find the absolute value in parenthesis.

Customizing  You can customize the function (F) keys below the screen by keying in  2nd   CUSTOM   F3(custom).   Use the arrow keys to scroll through the catalog putting the catalog arrow next to the item you would like to be able to access directly from the custom keys.  Once the arrow is there, press the function (F) key that you want to use, and the selected item will appear in the menu above that key.  Now exit back to the home screen.  To use your new key, press  CUSTOM, and the new menu will appear above your function key.  The root key is a good one to add to the custom keys.

Fractions To access the fraction convertor (converts decimal answer to a fraction), with the decimal you wish to convert on the home screen (it can be the answer to the previous calculation) press       2nd   X(MATH)   F5(MISC)    MORE   F1    ENTER.

Graphing with Restricted Domain  This is necessary for piecewise defined functions and functions that need domain restrictions to make them 1-1.   Type the function in parenthesis on the "y1=" screen.  In a second parenthesis type in the restriction.  The inequality symbols can be found under the TEST menu ( in yellow over the 2 key).  For piecewise functions, type in the first "piece" or rule with its domain restriction as explained above.  Then type + and enter the next function with its restriction and so on.  When you are finished typing, press more and look for "style" over the f3 key.   Press the f3 key until the style is a series of broken dots.  Now press graph and the function should graph with the appropriate restrictions.

    Example:  problem 47 in section 4 can be graphed by entering         y1 = (2x+3)(x<0)  +  (3-x)(x>0)   .  Select the dot style     and graph.

Greatest Integer Function  This can be found under the MATH menu (over the X key).  Choose NUM(f1) and IPART(f2).

INTERCEPTS:

x-intercept  The calculator function that finds x-intercepts is found under the graphing MATH menu (see MAX/MIN above).   The function you are looking for is root.  It works similarly to the MAX/MIN function in that you have to set a lower and upper bound so that the calculator will know which x-intercept to look for in case the graph has more than one.

y-intercept  This is also under the graphing MATH menu.  Use the more key to find YICPT.  There is no extra information required by the calculator because a function can have at most one y-intercept.

INTERSECTION OF GRAPHS

To find where two graphs intersect first graph the two functions.   On the window with the graph displayed press the MORE key, then F1 (MATH), then MORE, F3 (ISECT). The display will prompt "First Curve?" Put the cursor on one of the graphs you want to work with and press ENTER.  Then you get a prompt "Second Curve"?"  Put the cursor on the second graph you want to work with and press ENTER. Now you get a prompt "Guess?"  Move the cursor close to the point of intersection you want the coordinates for and press ENTER.  Repeat the process for other points of intersection.  To get the menu back press EXIT.  

Matrices (The plural of matrix)

To enter a matrix press the 2nd key followed by the 7 key (MATRX).  Choose F2(EDIT) to enter a new matrix or to edit an existing matrix.  When prompted give you matrix a name. I usually just type in a single letter, but you can make the name longer if you wish.  Press ENTER and tell the calculator the size of your matrix (Number of Rows x Number of Columns) pressing enter or the arrow key to move to the next position.  Type the numbers into the displayed  matrix.  Then EXIT. 

To perform calculations or operations on your matrix go back into matrix mode by using the 2nd 7(MATRX) keys. Look at your options under F3(MATH) and F4 (OPS)  and make a choice.  For example to get the reduced row echelon form of the matrix you entered choose F4(OPS) for matrix operations an select F5 (rref) for reduced row echelon form. Either type in the name of your matrix or go back to matrix, F1(NAMES) and select it from the menu.  Pressing enter should give you the rref.  (Also see systems of equations for solving systems of equations on the calculator without using matrices.)

MAX/MIN  After graphing the function, press MORE and f1 (MATH), and use the MORE key to find MAX or MIN whichever you need.  The calculator needs to know a point to the left (lower bound) and a point to the right (upper bound) of the maximum or minimum point you are looking for.  Use the arrow keys to position the cursor to the requested position and press enter.  You can mover the cursor close to the point you are looking for as a "guess", or you can just press enter twice after you give the upper bound.

REGRESSION

Draw a scatter plot of your data as outlined above.  EXIT back to the home screen and enter stat mode again by pressing 2nd + (STAT).  This time use F1(CALC).  The types of regression (best fit functions) which are available are listed over the F3, F4, F5, MORE, etc.  F3 (LinR) is linear and will find the line of best fit for the data you tell it to use.

After pressing F3 (LinR) press 2nd - (LIST) and F3 to get a display of the column names for the data you have entered.  The syntax is LinR xList,yList  where xList would be whatever column name you used for the "x" data and yList is whatever column name you used for the "y" data.  These should be displayed at the bottom of the screen after you chose 2nd - (LIST) and F3.  After choosing your column names, press ENTER.  This displays the equation and the correlation coefficient (corr or r) that your text refers to.

To see a graph of this line on your scatter plot, choose 2nd + (STAT) F4(DRAW) MORE F1(DRREG) for draw regression.

Forecast:  The 2nd + (STAT) MORE F1(FCST) feature allows you to enter values for either x or y and have the calculator solve for the other variable using the regression equation you just found.

Scatter Plots

Use 2nd + (STAT) F2 (EDIT). 

Use the arrow keys to go to the column headings (xSTAT and ySTAT).  Press the clear key while the column heading is highlighted.  When you arrow down the column entries will clear.

Enter your data into the xSTAT and ySTAT columns.  If you are adventuresome, you can use F3(NAMES) and name your columns of data rather than using xSTAT and ySTAT.

After you enter your data, use EXIT to get out of edit mode and then use 2nd + (STAT) to get back into stat mode.

F3(PLOT) ; then F1 (PLOT1); ENTER to turn the plot ON; arrow down to type and press F1(SCAT) to choose scatter plot (notice there are other choices of graphs such as HIST for histogram and xyLINE which connects the points with line segments).  After making your choice press ENTER to move to the Xlist.

For Xlist choose the column name (probably xSTAT) where the "x" (independent variable) data is stored.  Notice all the column names are listed over the function keys at the bottom of the screen. Press the correct F key and then press ENTER.

For Ylist choose the column name where the "y" (dependent variable) data is stored in the same manner as for xSTAT.

Now choose the symbol (Mark) you want to use in plotting the points by pressing the appropriate F key.

EXIT (press twice) out of STAT mode, and go into GRAPH mode.  Press F1(y(x)=) and then F4(DELF) to delete any functions that may be entered.  You can just deselect them with F5 or if you want them to graph on your scatter plot, just leave them.

Now use EXIT and then F3(ZOOM); MORE; and F5(ZDATA).  You should see your scatter plot.

WARNING!  When you go back to regular function graphing, be sure to go back and turn the plot off; otherwise, you are likely to get a domain error when you try to graph.

SYSTEMS of EQUATIONS

Press 2nd TABLE (SIMULT)  and enter the number of equations you are working with.  The calculator then prompts you for the coefficients of the first equation.  Notice that these are the same numbers that would be in row one of the augmented matrix that would represent the equations.  The calculator then prompts you for the coefficients of the remaining equations. When you have finished entering the numbers, press F5(SOLVE). The calculator returns solutions for x1, x2, x3, etc. rather than x, y, z, etc.  If you want solutions in fraction form use the fraction converter (FRAC).