Graphing Calculator Graphing with the TI-86

Transcription

1 Graphing Calculator Graphing with the TI-86 I. Introduction The TI-86 has fift kes, man of which perform multiple functions when used in combination. Each ke has a smbol printed on its face. When a ke is pressed the calculator does whatever is printed on the face of the ke. This is often referred to as the primar function of the ke. For eample, the primar function of the ON ke is to turn the calculator on, the + ke performs addition, and raises numbers to the second power. In addition to their primar functions man kes have second, or shifted functions. These are the smbols written in ellow and blue above the kes. To have the calculator do what is written in ellow ou must first press the nd (ellow) ke. To tpe letters into the calculator ou must first press the ALPHA (blue) ke. II. Plotting Points in a Scattergram We can use the calculator to create a scattergram of the data displaed in the table at right. As ou follow the steps below, compare the screen on our calculator to the screenshots to the right Press nd then STAT (STAT is a shifted function, press nd then the + ke). Your calculator window should look like the picture at the right. Press the F (EDIT) ke. If ou have an numbers (data) in the lists (Stat, Stat, or fstat) ou can clear them b pressing the up arrow to move the cursor to the top of the column, then press the CLEAR ke, followed b ENTER. Use or to get to the net list, and repeat the steps to clear all the lists. To enter the new data, enter the X-values from the table in Stat b tping ENTER, 5 ENTER, 8 ENTER, 11 ENTER. Move the cursor to Stat and enter the Y-values; 5, 8, 58, and 130 in the same wa. In the fstat column, enter 4 ones; that is a one for each data pair. To get to the plot menu, first press nd then STAT. Press PLOT (F3) to bring up the plot menu.

2 MLC MTH 070 Graphing With the TI-86 Press (F1) PLOT1, then ENTER to turn Plot 1 on. Note that Tpe, Xlist, Ylist, and Mark should all be set the same as the picture at the right. The Tpe shown is scattergram, the data list uses Stat for the X-values, Stat for the Y-values, and the points will be plotted as little squares as indicated b Mark. Press GRAPH to bring up the graphing menu. To adjust the window so that all the data points are in view we use a feature called ZDATA, or zoom data. To find that feature, first press ZOOM (F3). A sub-menu pops up below the zoom menu. Press MORE to advance the sub-menu to more choices. Press ZDATA (F5). This sets the window to fit the data points. Press EXIT. This removes one of the pop-up menus so that all the points in the scattergram become visible. III. Entering an equation Begin b pressing the GRAPH ke. The GRAPH menu appears on the screen and gives the following options: ()=, WIND, ZOOM, TRACE, GRAPH. These options are accessed b pressing the F kes located in the top row of kes. Notice the arrow to the right of GRAPH on the screen. This arrow indicates there are more options. Note: the and -aes ma appear on the screen. If the do, ignore them for now.

3 MLC MTH 070 Graphing With the TI-86 3 Press the MORE ke to see more on-screen menu options. Notice the arrow to the right of the RCDGB menu option. This means there are even more options. Press the MORE ke to see the remaining menu options. Press MORE again to return to the original menu options. Select ()= b pressing F1. the flashing rectangle net to \ 1 = is called the cursor. The cursor indicates where characters will appear when a ke is pressed. If there are epressions net to an of the \ 1 = use the ke to move the cursor to the line containing the epression and press CLEAR. Repeat as needed. Now with the cursor at \ 1 = enter +5. Use the -VAR ke or F1 to enter the variable. IV. Displaing Values in a Table We can use a calculator to displa a table of values for an equation that has been entered into the calculator. Press the TABLE button. Now press TBLST (F) to set up the table. TblStart is the first input value in the table and Tbl is the increment for the input values. Enter for TblStart (be sure to use the ( ) ke) and press ENTER. Then enter 3 for Tbl and press ENTER. Now press F1 to displa the table. Notice that the values start at and increase b an increment of 3. These are the instructions that ou gave the calculator in the previous window. You can scroll up or down the table using or.

4 MLC MTH 070 Graphing With the TI-86 4 V. Graphing an Equation Press M3 (nd, F3) to select the ZOOM menu, then select ZSTD b pressing F4. You should get the graph of = + 5. The ZSTD command tells the calculator to graph the equation in the standard screen. The standard screen includes the -ais from 10 to +10, and the -ais from 10 to +10. Verif this b pressing F to get WIND. This is the WINDOW screen. Xscl=1 means the -ais is scaled so that each mark is one unit. Notice the -ais is also scaled with one mark representing one unit. Press TRACE (F4). The calculator places the cursor on the graph of the line = + 5. The number 1 in the upper right corner of the screen indicates the number of the equation being traced, 1 in this eample. Move the cursor along the line b pressing or. Notice at the bottom of the screen the coordinates of the cursor are indicated b X = and Y= VI. Using Intersect to Solve an Equation. We can use the Intersect feature on the calculator to solve the equation 3 7 = 5. Go to the ( ) = window b pressing GRAPH and ( ) = (F1). If necessar, clear out an equations and turn plots off. Enter 3 7 in \ 1 = and enter 5 in \ =. To see the graph, press nd, GRAPH (F5). Notice the graph of 1 is a straight line with a slope of 3, and is a horizontal line. To find the point of intersection of the two lines, press MORE. Press MATH (F1).

5 MLC MTH 070 Graphing With the TI-86 5 Press MORE. Press ISECT (F3). The cursor appears on one of the graphs. You can tell which one b looking at the number in the upper right corner. The calculator prompts ou to tell it which two graphs (curves) ou are finding the intersection of. Press ENTER to indicate that the cursor is on one of our curves. The cursor jumps to the other graph and prompts ou with Second curve?. Press ENTER to indicate that the cursor is on the other curve. Now the prompt is Guess?, which is asking ou to place the cursor near the point of intersection. Use the, and kes to move the cursor close to the point of intersection and press ENTER. The cursor jumps to the point of intersection and the coordinates of that point are indicated along the bottom of the screen. VII Linear Regression Using the data in the table at the right, we ll use the calculator s linear regression feature to find a linear equation that best fits the data. First, we need to enter the data into the stat lists. If ou need to refresh our memor on how this is done, go to section II of this supplement and follow the first four steps of Plotting Points in a Scattergram When the data has been correctl entered our screen should look like the picture at the right. Press EXIT to return to the home screen, then press CLEAR.

6 MLC MTH 070 Graphing With the TI-86 6 To perform the linear regression function, first press nd then the STAT ke. We want to perform a calculation on the data, so press CALC (F1). Select LinR (F3) to perform a linear regression. Note there are other tpes of regression besides linear. In this window the options include eponential regression (EpR (F5)) and quadratic regression (MORE, PReg (F4)) among others. Press ENTER to perform the regression. This output describes a linear equation with slope 11.5 and -intercept -14.5, so the equation is = We are not going to use the corr= for our purposes. To graph the regression equation along with the scattergram, first plot the scattergram b turning on plot 1 and pressing GRAPH, ZOOM, MORE then ZDATA (F5). If ou need to refresh our memor on these steps, go to section II, Plotting Points in a Scattergram, and read steps 5 through 8. Press ()=. Be sure that all equations are cleared and the plot is turned on. When we perform regression, the equation is stored as a statistics variable named RegEQ. We graph the regression equation b inserting RegEQ into the = window. First, to find RegEQ, press nd then CATLG-VARS (CUSTOM). Press the MORE ke twice. Press STAT (F4)

7 MLC MTH 070 Graphing With the TI-86 7 Select RegEQ b pressing the down arrow ke four times. Press ENTER. This inserts the regression equation into the ()= screen for graphing. Press nd, then GRAPH (F5). We can see the regression line along with the scattergram of the data. VIII. Finding the -intercepts of a graph Clear the previous equations and enter the equation = 6. Graph the equation. Be sure the window is set so that ou can see all of the -intercepts. In this eample use the standard window. Press MORE then MATH (F1). We are looking for the - intercepts of a quadratic, which are also called roots. Press ROOT (F1). Notice that the cursor is flashing on the screen at the point (0,-6). The calculator will onl look for one -intercept at a time and it will onl look for one within a range of values that ou must specif. Left Bound? on the screen is a prompt for ou to enter the smallest value in the range. Use to move the cursor to the left of the leftmost -intercept and press ENTER. The right-pointing black triangle on the screen indicates the smallest value the calculator will consider in looking for an -intercept. Right Bound? on the screen is a prompt for ou to enter the largest value in the range. Use to move the cursor to the right of the leftmost -intercept and press ENTER. The left-pointing black triangle on the screen indicates the largest value the calculator will consider in looking for an -intercept. You should have placed the left and right bounds to that there is one and onl one -intercept between the

8 MLC MTH 070 Graphing With the TI-86 8 triangles horizontall. Guess? is a prompt for an value in the specified range that the calculator can use to start its search algorithm. An - value in the range will work. If ou press ENTER the calculator will use the coordinate of the current position of the cursor. Since the cursor is at the right bound, that value is valid. Press ENTER. The cursor is flashing on the - intercept and its coordinates are listed at the bottom of the screen: (,0). Repeat the procedure to find the other -intercept. IX. Problems for Practice Use a calculator to make a scattergram of each of the following data tables Use a calculator to make a table of values for the following equations. Use TblStart= 10 and Tbl=5 3. = = Use a calculator to draw the graphs of the following equations. 5. = 3( ) 6. = 5 + ( 1) 7. Use the Intersect feature to solve the equation; 3= 4 8. Find the point of intersection of the graphs of = 5( +1) and = ( + 3) 9. Use linear regression to find a model of best fit (equation) for each of the tables. Graph the regression model and the scattergram in the same window. Round decimals to two places. a) b)

9 MLC MTH 070 Graphing With the TI Find the -intercepts of = Answers: (standard window) = 3.5, = a) = b) =