page 1 TI-89 Calculator Workshop #1 The Basics After completing this workshop, students will be able to: 1. find, understand, and manipulate keys on the calculator keyboard 2. perform basic computations 3. enter and edit expressions 4. produce and manipulate graphs of functions Note: This workshop is designed for students in MAT 109 and above. The TI-89 Viewing Screen (insert screen here) When you turn on your calculator, the viewing screen should look similar to the screen shown above. If your screen looks different, hit the HOME key (1 st column, below the green diamond key) to obtain this screen. At the top of the screen, you ll see pull-down menus labeled F1 (Tools), F2 (Algebra), F3 (Calc), F4 (Other), F5 (PrgmIO), F6 (Clean Up). These menus make up the toolbar. Press the blue F1 key at the top of your keyboard. What options do you see? To return to the home screen (that shown above), select either the blue ESC key (2 nd row, 3 rd column) or HOME. Below the F menus, you ll see an area taking up most of the viewing screen. This is the history area. In the history area, you ll see expressions and calculations you ve previously entered. To clear this part of the screen, select the blue F1 key (Tools) and either arrow (using blue arrow keys on the top right of your keyboard) down to option 8 (and hit enter) or type 8. The narrow strip below the history area displays the expression you are currently entering. This strip is called the entry line. Enter the keys 2, +, 3. What appears in the entry line? What happens when you hit the blue Enter key (bottom right of your keyboard?)
page 2 Below the entry screen are indicators of your current calculator modes in the status line. You should see the word main at the bottom left of your viewing screen. This means your calculator is in its main state. Other indicators will tell you how the calculator is treating expressions you enter. The Keyboard F keys: These blue keys are located in the first row of your calculator and allow you to access pull-down menus that appear at the top of your screen. Pressing the blue keys allows you to access the menus entitled F1 through F5. To access the F6 menu, press the yellow 2 nd key in the second row, then F1. Yellow 2 nd key: This key is located in at the beginning of the second row and allows you to access values and operations in yellow printed above most keys. To use it, hit 2 nd and then the key below the function/value you wish to access. What function would you access by typing in 2 nd X? Blue ESC key: This key allows you to escape from menus or dialog boxes. For example, if you pull down the Tools menu (F1) and decide you don t want to select any of the options within that menu, you can hit the ESC key to return to the screen you were at previously. Green diamond key: This key allows you to access commands and functions printed in green above the standard keys. Purple alpha key: This key allows you to type lower-case letters printed in purple above the standard keys. To type an upper-case letter, hit the black and white arrow key to the right of the 2 nd key before typing the letter. To type multiple lower-case alphabet letters, hit 2 nd alpha (to access alpha lock ). To type multiple upper-case letters, hit the arrow key, then alpha. To turn off the alpha lock, hit alpha again. HOME key: This key is located in the 4 th row of your keyboard and allows you to return to the home screen at any point. The home screen is the screen you see when you turn on your calculator. MODE key: The mode key allows you to change the way your calculator is treating the expressions that type into the entry line. What appears when you select the MODE key? pages? Access pages 2 and 3 in MODE. What choices do you have on these
page 3 CATALOG key: This key allows you to access basic functions and procedures, such as the absolute value function abs(, drawing a circle Circle, conversion functions, factoring factor, and more. Back arrow key: This key allows you to backspace within the entry line. CLEAR key: This key allows you to clear all or part of the expression you ve entered in the entry line. Blue arrow keys: These keys allow you to move the cursor around within the keyboard. Within the expression, you can arrow left and right. Within menus, you can arrow up and down. X, Y, Z, and T: These keys allow you to enter variables into your expression. ^: This key allows you to raise numbers and expressions to an exponent. For example, 3^4 is 3 to the fourth power. EE: This key allows you to enter numbers in scientific notation. To enter 5.32 x 10^8, for instance, type 5.32 EE 8. (-): This key allows you to apply a negative sign to a negative number. It cannot be used to indicate subtraction. Similarly, the subtraction key - cannot be used to indicate a negative number. Please be very careful when choosing between this key and the subtraction - key. If you choose incorrectly, you ll get a syntax error on your calculator. Basic Calculations Almost all basic calculations can be performed on your TI-89. Most calculations are performed when you enter the expression in the entry line and hit Enter. The TI-89 follows order of operations. Try entering the following expressions and write down the resulting values: 2 3(4 2) 1 3 2(1) 8/ 2 = [(3 2) (4 5)] 4(5) 9(2) 3 4 =
page 4 100 5( 7) 4(20) = Editing Expressions Suppose you type in the expression 3(3 2) 24 6, but meant to type in the expression 3(3 2) 24/ 6. If you catch your mistake before you hit Enter, you can use your left arrow key to place your cursor just to the right of the - sign. You can then select the back arrow key (the black key, not the blue arrow key), to backspace over the subtraction sign. Next, type in / (the divide sign on your keyboard). Your calculator will automatically insert this character between the 4 and the 6. You can also move your cursor to the left of the subtraction sign and select green diamond, Del (backarrow key). If you ve already hit Enter, you can access the previous expression by hitting 2 nd Enter. Then you can edit the expression as described above. Enter the expression (2 3) 2 4/ 5. What is the result? Oops! You meant to enter (2*3) 2 4* 5. Use 2 nd Entry to obtain the expression again. Edit the expression to that above. What is your result now? Notice the x/30 indicator at the right hand side of the status line. The x indicates the number of expressions you have entered, and 30 is the maximum number available for retrieval. To lighten or darken the contrast on your viewing screen, you can enter green diamond - or green diamond +, respectively. This may be done multiple times to obtain the desired contrast. Imagine you would like to evaluate 2/3. Enter 2 / 3 on your calculator and hit Enter. What is the result? But, you already know that. You d like to know the decimal equivalent. There are several ways to obtain an answer in decimal (or approximate) form. The first way is to change your mode. Select MODE, and use the F2 key to get to the second page. Here, you ll see the Exact/Approx option. Arrow down to this option, and arrow to the right. You ll see the options Auto, Exact, and Approximate. Most likely, your calculator is in Auto mode (confirmed by the status indicator in the status line of your home screen). The auto option displays your numbers exactly when
page 5 possible (when the number can be represented as a fraction or as a function of roots and transcendental numbers such as pi and e) and as approximate numbers (or decimal numbers) otherwise. 2/3 is an exact number. If you want the decimal equivalent, you want the approximate number. So, you can switch your mode to Approximate and redo the calculation. There is another way to find the approximate (decimal) answer without switching from Auto. (Auto is a nice mode, because it automatically chooses the most appropriate mode for your answer.) To find the decimal approximation, you can divide your answer by 1.0 (or a decimal) to get a decimal answer. Or, you can enter the expression as 2./3, 2/3., 2./3., 2.0/3, etc. to indicate that one of the numbers is approximate (thus having a digit (implied or actual) after the decimal point). Multiply the expression 2/3 obtained above by 1.0 (or 1.). What do you get? The TI-89 calculator performs operations with fractions. It can add, subtract, multiply and divide fractions, leaving the answer in fraction form (given that the calculator is in auto or exact mode). Add ½ and ¼. What answer do you get? Basic Graphing 2 To graph a basic function, like y f ( x) x, do the following: 1. Hit green diamond F1 (to get Y=) 2. You should see a screen with y1 =, y2 =, etc. Move your cursor to the right of y1=, hit Enter, and type in the function x^2 (using the X key for the variable x) in the entry line. 3. To graph this function, hit the green diamond key again, followed by F3 (Graph). Draw a picture of the graph you see in your viewing rectangle: (insert basic graph screen here) To determine the range of values graphed, select diamond and F2 to get to the Window option. These values are the smallest and largest x- and y-values shown in your viewing rectangle. What is your range for the graph of f(x) = x 2?
page 6 Oops! You ve entered your function incorrectly. Or perhaps you d like to change the y- intercept of your function. To edit the function you ve entered and graphed, return to the y = screen. If the function you wish to edit is not highlighted, use the up and down arrow keys to highlight that function. Once it s highlighted, hit enter and you ll see the highlighted expression in the entry line. Use the left or right arrow key to move the cursor to the left or the right of the function. At this point, you can edit to your heart s desire. Zooming In and Out You may want to zoom in or out on the graph of a function. To do so, select F2 for the zoom menu. Select option 2, or ZoomIn (again, you can select by either arrowing down to option 2 and hitting Enter or hitting the 2 key). You will be asked to determine the center. Leave it as is, and hit Enter. : What happens to the graph of x 2? You zoomed in on your graph, but how much? To determine the range of your graph, go back to the Window option. What is the range of the graph of f(x) = x 2 after you zoom in once? To return to the original viewing rectangle, select ZoomStd (zoom standard), or option 6. : Choose other zoom options (except ZoomBox) and describe what happens to the graph (you may need to look at the Window values to determine what has happened): ZoomOut ZoomSqr ZoomTrig 3 2 Now, try graphing f ( x) 3. Pull down the Zoom menu again, and select ZoomBox. You ll be asked to select the 1 st corner. Use the arrow keys to move to the upper left hand corner of the area of the graph that you re interested in viewing. Hit Enter when you arrow to the corner. Then use your arrow keys to move the second corner of the box to the bottom right hand corner of the area of the graph you d like to view. Hit Enter.
page 7 What happens to your graph? Tracing the Graph: The trace option (F3) allows you to trace your graph using the left and right arrow keys. Notice that x- and y-values at the bottom of the screen correspond to the cursor s location on the graph of the function. First, use the ZoomStd zoom option to revert back to the standard viewing window. Then select the Trace option. What y-value is shown when you trace to a x-value of 1? Evaluating and Analyzing Graphs of Functions F5 allows you to explore properties of the graph of a function. The 1 st option, Value, allows you to evaluate the function at any x-value. Choose Value and an x-value of 3. What is the function value? (Note that your viewing rectangle, or Window must contain the x-value of the point on the graph you wish to evaluate. If you see a Window variables domain mistake, change your viewing rectangle either through a Zoom option or through the Window screen.) You can also find maximum and minimum y-values of the graph shown in your viewing rectangle. To do so, select F5, then Minimum or Maximum. You will be asked for lower and upper bounds. For the lower bound, use your left and right arrow keys to move your cursor to the left of the maximum or minimum value you want to determine. Hit enter to select the lower bound. Repeat this procedure for the upper bound, except that your cursor should be placed at the right of the minimum or maximum. Once you ve selected your lower and upper bounds, the maximum or minimum will be shown. 3 2 Find the maximum and minimum values of f ( x) 3 in the standard viewing rectangle. The maximum y-value is and is located at the x- value. The minimum y-value is and is located at the x-value. You can also find the intersection points of two or more curves. Graph a second function f ( x) 3x 2 in the same viewing rectangle. Notice that there appear to be three intersection points. To find the first, select F5, then 3 2 Intersection. The cursor should be located on f ( x) 3 and the bottom of the screen should say 1 st Curve?. Since this is your first curve, hit Enter. The cursor
page 8 should then be located on f ( x) 3x 2 and the bottom of the screen should say 2 nd curve? Since this is your second curve, hit Enter. (Note that if you have more than two curves, you can select curves by using the up and down arrows). You will be asked to select lower and upper bounds. Select x-values to the left and right of the first intersection point on your graph and hit Enter. What are the coordinates of the first intersection point? Repeat the procedure for the second intersection point. What are the coordinates for the second intersection point? Repeat for the third intersection point. What are the coordinates for this intersection point? You can also find roots/zeroes of functions using the F5 option. To do so, select the Zero option and use your up and down arrow keys to select the appropriate function. Then enter lower and upper bounds and hit Enter. List all zeroes for the function f ( x) 3x 2: 3 2 List all zeroes for the function f ( x) 3 : The table function allows you to examine a table containing x- and y- values for functions. Select diamond F5. What is displayed? The settings for tables can be adjusted using the TblSet key ( diamond F4). The starting x-value of the table can be changed, and the differences between subsequent x- values can be adjusted. The independent option allows the table to be set up so that x- values can be individually entered instead of automatically generated. To set up the table this way, select option 2, ask. (Derivatives, integrals, inflection, parametric, polar graphing, etc. will be highlighted in the Calculus workshop) Basic Algebra Your TI-89 can perform many basic algebraic procedures. The F2 key allows you to factor expressions, solve equations, simplify expressions and find zeroes/roots of functions. To factor an expression, select F2, then factor(. You should see factor( on the entry line. After the open parenthese, type in your expression and close the parentheses. Hit Enter and your expression should be factored.
page 9 Factor x 2 4: Factor 3x 2 7x 6 : Factor 5x 2 7x 1: What does the answer to the third expression indicate? To solve an equation, select F2, then solve(. In the entry line, type in the equation after (, followed by a comma, then the variable for which to solve, and close the parentheses and hit Enter. Solve 3x 4 20: 2 2 Solve 3x 4y 20 for y: To simplify an expression, select F2, then expand(. Behind (, type in the expression to be simplified, close the parentheses, and hit Enter. 3 Simplify 3x ( x 4) 4x x (2x 2) : To find the zeroes of a function, select F2, then zeros(. Type in the function for which you want to find zeroes, a comma, and then after the ( and hit Enter. Find the zeroes of f 5 4 3 2 ( x) 3x x : To solve systems of equations, use the rref function. (This command refers to reduced row echelon form a matrix-based procedure for solving systems of equations). In order to use this function, you must first reduce your system of equations to a matrix. For example: 3x 4y 10 x 2y 5 reduces to the matrix 3 1 4 10 2 5. This is the matrix that will be entered into the command. The format is rref ( [ 3, 4, 10; 1, -2, 5 ]). The square brackets indicate that you re entering a matrix. The semi-colon indicates that end of one row and the beginning of the next. The rref command can be found in the Catalog. To find the function quicker, you can type in the first letter of the function (here, R) once you re in the catalog. (Note that R is the 2 key). Solve the system given above: x = y = This technique can be extended to larger systems of equations.