Using the Function Table Feature A function can be displayed in a table of values. 1. Enter the function into the data entry line of the Graphs and Geometry application. For example, to enter the function y 5 20.1x 2 1 2x 1 3, press. 2. Add the Lists and Spreadsheet application. Press, and scroll to 3: Lists & Spreadsheets Application. Press. 3. View the function table. Press, and scroll to 5: Function Table 1: Switch to Function Table. Press press to select the choice, then again to carry out the request.
4. Set the start point and step size for the table. It is possible to view the table with different increments. For example, to see the table start at x 5 23 and increase in increments of 0.5, press, scroll to 5: Function Table 3: Edit Function Table Settings and press, and then adjust the settings as shown. Then to OK and press. TI-83/84
Using the Split Screen 1. To see a graph and a table at the same time: press. Scroll to 5: Page Layout 2: Select Layout 2: Layout 2 (your choice), and press. Press followed by to move the cursor to the empty screen. Press to select the Lists and Spreadsheet application, and press. Press and scroll to 5: Function Table 1: Switch to Function Table. Press press to select the choice, then again to carry out the request. TI-83/84
Determining the Zeros of a Function To determine the zeros of a function, use the Trace feature in the Graphs and Geometry application. 1. Enter the function. Enter y 5 21x 1 32 1x 2 52 into the data entry line of the Graphs and Geometry application. Press. 2. Access the Trace feature. Press and scroll to 5: Trace 1: Graph Trace, then press. 3. Use the and keys to move the cursor along the curve. A point will appear on the graph. Using the cursor, move the point until the word zero is displayed. Repeat to determine the second zero. TI-83/84
Determining the Maximum or Minimum Value of a Function The least or greatest value can be found using the Trace feature in the Graphs and Geometry application. 1. Enter y 5 22x 2 2 12x 1 30. Graph the function and adjust the window as shown. The graph opens downward, so it has a maximum. 2. Access the Trace feature. Press and scroll to 5: Trace 1: Graph Trace, then press. 3. Use the and keys to move the cursor along the curve. A point will appear on the graph. Move the point until the word maximum is displayed. If a graph has a minimum, the point will be displayed with the word minimum. TI-83/84
Determining the Points of Intersection of Two Functions 1. Enter both relations into the data entry line of the Graphs and Geometry application. For example, enter y 5 5x 1 4 in f1(x), and then press. Enter y 5 22x 1 18 in f2(x), and then press. 2. Graph both relations. Adjust the window settings until the point(s) of intersection is (are) displayed. You can do this by changing the window settings or by picking up the graph and moving it. Move the cursor to an empty area in the window. Hold the click key down until a closed fist appears. Use the arrow keys to move the graph until you see the intersection point(s). 3. Use the intersection feature. Press and scroll to 6: Points & Lines 3: Intersection Point(s), and then press. 4. Determine a point of intersection. Select the two lines. Move the cursor to one of the lines. When the line blinks, press to select the line. Repeat this process to select the second line. As you move the cursor near the second line, a point will appear at the intersection. To make the point permanent and to know its coordinates, press. The point of intersection is (2, 14). Note: If there is more than one point of intersection, all the points of intersection that are visible in the window will appear. TI-83/84
Adjusting the Number of Digits Displayed To determine the lower zero of the function y 5 x 2 1 x 2 5 to four decimal places, you can change the number of digits displayed for a particular value on a graph, for all values on graphs, or for all calculated values generally. 1. Graph the function and determine the lower zero. In the Graphs and Geometry application, enter the function y 5 x 2 1 x 2 5. Press and scroll to 6: Analyze Graph 1: Zero to determine the lower zero of the function. 2. Change the number of digits displayed for the zero. Move the cursor over the coordinate label for the zero. It will change to a hand icon with text next to it. Press and scroll to 2: Attributes. Use the or key to change the number in the Custom Precision box to 4, then press. Alternatively, 3. Change the number of digits displayed for all values. Move the cursor to the icon near the top right of the screen and click on it: scroll to 2: Settings 2: Graphs and Geometry to change the number of digits displayed in the Graphs and Geometry application only, or scroll to 2: Settings 1: General to change the number of digits displayed by the handheld in all modes. For four decimal places, click on the Display Digits scroll down, and click on Fix 4. Then, click on OK. arrow,
Evaluating Trigonometric Ratios and Determining Angles 1. Put the handheld in degree mode. Press. Select 8: System Info 1: Document Settings. Use to move through the selections. At Angle, select Degree using the key. Press to select Degree. Continue to press until OK is selected. Then press. Press and select the calculator application. 2. Use the,, or key to calculate trigonometric ratios. To determine the value of sin 45, press. The answer will be exact. To determine the decimal approximation, press, then.
3. Use SIN 21, COS 21, or TAN 21 to calculate angles. To determine the angle whose cosine is 0.6, press. TI-83/84
Evaluating Powers and Roots Use the calculator application. 1. Evaluate the power 5.3 2. Press. 2. Evaluate the power 7.5 5. Press. 3. Evaluate the power 8 22. Press. 4. Evaluate the square root of 46.1. Press. TI-83/84
Solving Quadratic Equations To solve the quadratic equation 3x 2 2 2x 2 5 5 0, you can use the polyroots function. 1. In the Calculator application, call the polyroots function from the Algebra menu. Press and scroll to 3: Algebra 3: Polynomial Tools 2: Real Roots of Polynomial. 2. Enter the corresponding quadratic function. Press. The real roots of the function are returned, if they exist. If there are no real roots, { } is returned. With the TI-Nspire CAS handheld, it is also possible to solve quadratic equations algebraically by various methods.
Graphing Inequalities The relationship between the number of pairs of skis, x, the number of snowboards, y, and the daily sales for a sports store can be represented by the inequality 100x 1 120y. 600 or y. 2 5x 6 1 5 1. Enter the inequality, with y isolated. y. 2 5x 6 1 5 With the cursor to the right of the 5 sign, press. Select > from the pop-up menu that appears. Then enter the right side of the inequality, 2 5x 6 1 5. 2. Adjust the screen to show the first quadrant only (optional). In this case, the variables are whole numbers, so it is appropriate to show only the first quadrant. Press and scroll to 4: Window/Zoom 1: Window Settings. Change to the settings shown and click on OK or just press. The boundary is a dashed line because the > inequality sign was used, meaning that the solution set does not include values on the boundary.
Plotting Points Plot the test point (4, 4) for the inequality y. 2 5x 6 1 5 1. Create a point. Press, scroll to 4: Points & Lines 1: Point, and click or press. A pencil appears with which you can place the point approximately. 2. Edit the coordinates of the point. To locate the point exactly at the coordinates (4, 4), move the cursor over it. The cursor will change to a hand icon with text next to it. Press and scroll to 7:Coordinates and Equations. A label will appear next to the point with its current coordinates. Double-click on each coordinate in turn, changing it to 4 and pressing. The point will now be plotted and labelled at (4, 4). GSP
Entering Data The following frequency table shows the lengths of Emmanuella s walks with her golden retriever during one month. To work with this data, you will need to enter it into a spreadsheet and also calculate midpoints for the intervals. Length of Walk (min) 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 55 55 60 Frequency 1 3 7 10 6 11 8 5 4 2 3 1. Set up column names. To enter the data above in the Lists and Spreadsheet application, begin by labelling column A lower, column B upper, column C1 midpoint, and column D freq. 2. Enter the data. Enter the data from the frequency table in columns A (lower limits of intervals), B (upper limits of intervals), and D (frequencies). In cell C1, enter the function command (A1 B1)/2. Then, copy or fill down this entry for the rest of the cells in column C, down to the last line of the data. The cell addresses will automatically adjust. The spreadsheet now shows the midpoints as well as the intervals and frequencies for the data. TI-83/84 Spreadsheet Fathom
Determining Mean, Median, Mode, Range, and Standard Deviation In the Lists and Spreadsheet application, enter the following data in a single column: Unit 1 Test 81 76 73 71 64 80 75 73 71 63 79 75 73 68 61 79 74 73 67 58 78 73 72 66 57 1. Determine the mean, standard deviation, and median of the data. Select column A by clicking on the small A at the top left of the column. Press and scroll to 4: Statistics 1: Stat Calculations 1: One-Variable Statistics. Press to display the single-variable statistics for column A. Row 2, showing x and 71.2, gives the mean for the data. Scrolling down, row 6, showing x : and 6.548, gives the standard deviation for the data. Row 10, showing MedianX and 73, gives the median for the data. 2. Determine the range of the data. Rows 8 and 12 give the minimum and maximum values for the data. The range is the difference of these two values. Enter range in cell D8 and =c12 c8 in cell E8, which now displays the range of the data.
3. Determine the mode of the data. To determine the mode, it is helpful to sort the data. Select column A, press, and scroll to 8: Sort. Adjust the settings if necessary to show a and Ascending, then click on OK or just press. The data in column A will now be sorted from least to greatest values. Scroll through column A and determine the mode by locating the value(s) that occur most frequently. In this case, the mode is 73. TI-83/84 Spreadsheet Fathom
Determining the Mean and Standard Deviation of Grouped Data The following frequency table shows the lengths of Emmanuella s walks with her golden retriever during one month. First, enter the data into a spreadsheet and calculate midpoints for the intervals, as shown in Entering Data. Length of Walk (min) 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 55 55 60 Frequency 1 3 7 10 6 11 8 5 4 2 3 1. Determine the sum of the grouped data. Create a new column named f.x in column E. In cell E1, enter d1 c1. To copy this down for each data row, Press with E1 selected, then scroll to 2: Copy and click or press. Select cells E2 through E11 and press to paste in the same formula for the whole data range. The cell addresses will automatically adjust. Then, in cell E12, enter sum(e1:e11). 2. Determine the mean of the grouped data. To determine the value of n, sum the frequencies by entering sum(d1:d11) in cell D12. Then, scroll over to cell G1 and enter e12/d12 to determine x 5 a f x. n This displays the mean of the grouped data. 3. Determine the sum of the squared deviations. First, enter g1 in cell G2, and copy this down through to cell G11. (This will make calculating the square deviations easier.) Then, create a new column named f.sqdev in column F. In cell F1, enter d1*(c1-g1)2. Copy this down for each data row, then edit. Then, in cell F12, enter sum(f1:f11).
4. Determine the standard deviation of the grouped data. Enter sqrt(f12/d12) in cell H1 to to determine a s5 f 1x 2 x 2. É n This displays the standard deviation. Spreadsheet Fathom
Creating a Histogram The following frequency table shows the lengths of Emmanuella s walks with her golden retriever during one month. First, enter the data into a spreadsheet and calculate midpoints for the intervals, as shown in Entering Data. Length of Walk (min) 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 55 55 60 Frequency 1 3 7 10 6 11 8 5 4 2 3 1. Select the data to graph. Select columns C and D, which contain the midpoints and frequencies for this data. Click on the small C at the top left of column C, then press to select column D as well. 2. Create a histogram. Press, scroll to 3: Data 5: Frequency Plot, press, and then click on OK. A histogram will appear on the right side of the screen. TI-83/84 Spreadsheet Fathom
Creating a Frequency Polygon The following frequency table shows the lengths of Emmanuella s walks with her golden retriever during one month. First, enter the data into a spreadsheet and calculate midpoints for the intervals, as shown in Entering Data. Length of Walk (min) 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 55 55 60 Frequency 1 3 7 10 6 11 8 5 4 2 3 1. Select the data to graph. Select columns C and D, which contain the midpoints and frequencies for this data. Click on the small C at the top left of column C, then press to select column D as well. 2. Create a frequency polygon. Press, scroll to 3: Data 6: Quick Graph, press, and then click on OK. A graph will appear on the right side of the screen. Place the cursor over the graph, press, and select 2: Connect Data Points to form the frequency polygon for the data. Spreadsheet Fathom
Using the Normal Cdf Command To determine the proportion of data from 161 cm to 197 cm on a normal distribution of heights of students with mean 177 cm and standard deviation 15 cm, use the normalcdf command. 1. Select the normalcdf command. In the Calculator application, press and scroll to 6: Statistics 5: Distributions 2: Normal Cdf. A dialog box will appear for the Normal Cdf function. 2. Enter the argument. Enter the given data as shown. Then, click on OK or just press. The proportion of data between 161 cm and 197 cm is displayed as a decimal, in this case 0.765... or about 76.6%. 3. Use the normalcdf command with a standard normal distribution. If the data points are z-scores, so you are using a standard normal distribution with mean 0 and standard deviation 1, you can leave the mean and standard deviation as their default values in the Normal Cdf dialog box, and just enter the area. TI-83/84 Spreadsheet
Using the Inverse Normal Command A brand of running shoes lose their shock absorption after a mean distance of 640 km, with a standard deviation of 160 km. Zack plans to replace his shoes when there is only a 25% chance that they have lost their shock absorption. At what distance should Zack replace his shoes? 1. Select the Inverse Normal command. In the Calculator application, press and scroll to 6: Statistics 5: Distributions 3: Inverse Normal. A dialog box will appear for the Inverse Normal function. 2. Enter the argument. Enter the given data as shown. Then, click on OK or just press. The appropriate distance is displayed, in this case 532.082 km. 3. Use the invnorm command with a standard normal distribution. For a standard normal distribution with mean 0 and standard deviation 1, you can leave the mean and standard deviation as their default values in the Inverse Normal dialog box, and just enter the z-score. TI-83/84 Spreadsheet