!"### Functions are entered from GRAPH Mode into the Y= screen and are referred to by name as Y1, Y2,..., Y19, Y20. To evaluate a function for a particular x-value, for example, Y1 when x = 4, from RUN Mode, press [4] [ ] [x,θ,t] [EXE] to assign a value of 4 to x. Then press [VARS] [F4] (GRPH) [F1] (Y) [1] [EXE] to see the value of Y1.! %#&#' With bits of tape, label two EA-100s A and B. Label two calculators A and B, and connect each to the respective EA-100. From the PRGM Mode, highlight the program MOVIN, and follow the on-screen instructions. For both calculators, the time data will be in List 1 and the distance data will be in List 2. From the RUN Mode of calculator B, press [OPTN] [F1] [F1] [1] {List 1} [ ] [F1] [3] {List 3} [EXE]. Then press [F1] [2] {List 2} [ ] [F1] [4] {List 4} [EXE]. This moves calculator B s time and distance data to List 3 and List 4. Finally, each group member should link to calculator A and copy List 1 and List 2, and link to calculator B and copy List 3 and List 4. See Note 1J for help with linking lists.!"#'() #'* When you trace a function or locate a point on the screen, you often see long, ugly decimal values for the coordinates of your points. Sometimes, however, the values are nice, friendly values, like 2.4 or 4.84 or repeating decimals like 4.3333333. When the proper values are set for Xmin and Xmax in the View Window screen, the coordinate values of your points will be friendly numbers for most functions. This is because the calculator screen is made of tiny square dots called pixels, and when you move horizontally across the screen, the x-coordinate changes by one pixel with each trace step. The total number of pixels across the screen is 127; in other words, it takes 126 steps to get across. When 126 is either equal to or a multiple of the breadth of the domain Xmax - Xmin, the window will be friendly. For example, if Xmin = 0 and Xmax 22
= 126 or Xmin = 1 and Xmax = 13.6, the window will be friendly. (Note: The y- coordinate is calculated by evaluating the function for the x-coordinate. So if the coefficients in a function are irrational, the y-coordinates will not be nice even in a friendly window.) Two Friendly Square Windows If you press [SHIFT] [F3] [F1] (INIT), you get a special type of small friendly window called a friendly square window. It is friendly because it has the view window values [-6.3, 6.3, 1, -3.1, 3.1, 1]. It is square because the horizontal and vertical scales on the screen are equal in size. In a square window, circles appear symmetric and round and the line y = x makes a 45-degree angle with both axes. A square window is often the preferred window to use because it displays no visual distortion. However, this window, [-6.3, 6.3, 1, -3.1, 3.1, 1], is sometimes too small to show much of the graph. To see more of the graph in the window, you can double the Xmin, Xmax, Ymin, and Ymax values, [-12.6, 12.6, 1, -6.2, 6.2, 1]. This square window is referred to as the friendly window with a factor of 2. The friendly window with a factor of 2 is often a convenient window to use. To save it and recall it quickly, follow these steps. a. First enter the values [-12.6, 12.6, 1, -6.2, 6.2, 1] into your View Window screen. b. Then from the View Window screen, press [F4] (STO) [F1] (V-W1). Note: Up to five more windows can be stored by using the other function keys. c. The next time you need this window, say for the graph of y = x 2, press [SHIFT] [F5] (RCL) [F1] (V-W1). 23
Other Friendly Square Windows To assure that a window is square, the size of a horizontal step, called x, must equal the size of a vertical step, called y. x is the step size of the trace. In the square window [-6.3, 6.3, 1, -3.1, 3.1, 1], x is 0.1. In the square window [-12.6, 12.6, 1, -6.2, 6.2, 1], x is 0.2. Values for origin-centered friendly square windows are: [-63 x, 63 x, 1, -31 y, 31 y, 1]. For example, if x and y equal 0.3, then... First-quadrant friendly square window values are [0, 126 x, 1, 0, 62 y, 1]. Again, if x and y equal 0.3, then... Friendly Windows That Are Not Square The Ymin and Ymax values of a friendly window can be changed to show a larger or smaller range. The graph will look distorted and it will no longer be square, but this might be necessary to see more of the graph. For example, the graph of y = x 2 in the friendly square window [-12.6, 12.6, 1, -6.2, 6.2, 1] runs off the top of the graph for x- coordinates greater than 2.4. If you want to see more of the graph, change the window to [-12.6, 12.6, 1, -10, 100, 10]. This is a friendly window because the coordinates are still nice, but it is not square. 24
You can also see more of a graph without first changing the view window settings. Without using the trace option, press an arrow key to automatically scroll the graph in any direction. As you scroll, the view window settings change to reflect the current screen. +!#,- ##'-.# Transformations of Functions You can graph multiple, transformed versions of the same function on the same screen. Suppose you want to translate the graph of y = x 2 horizontally to the right 3 units, to the right 5 units, and to the left 1 unit. Perform the following steps: a. From the GRAPH Mode, enter (x-a) 2,[A=0,3,5,-1] into Y1 in the Graph Function menu (Y= screen). b. Press [F6] (DRAW). Watch the four functions as they are plotted to see which is associated with which translation. Press [EXIT] and [F6] (DRAW) to repeat the plotting. c. Press [F1] (TRCE) to trace on the graph. The left and right arrow keys move the cursor along one of the graphs. The up and down arrow keys move the cursor from one function to another. Similarly, you can show the graph of y = x 2 and the two transformations: a reflection across the x-axis followed by a vertical stretch by a factor of 3 and a reflection across the x-axis followed by a vertical stretch by a factor of 0.5. Enter -Ax 2,[A=-1,3,0.5] into Y1 and draw the graph.!" /- The program TRANSFRM gives you practice finding equations for given graphs. From the first menu, choose the type of function you want to practice. Then you will be prompted to choose whether you want to practice translations, reflections, dilations (stretches), or any combination of the three. The calculator will display a graph and stop. 25
Study the graph and determine its equation. Press [SHIFT] [F1] (TRACE) if you want to see the coordinates of points. When you have decided on an equation, press [MENU] [5] to enter the GRAPH Mode. Enter your equation into Y1, and press [F6] (DRAW). If your equation is correct, you ll have a match and nothing new will appear on the screen. If your equation is not correct, the graphs will not match. In that case, press [EXIT] and try again. When you are finished with one graph, choose PRGM from the MAIN Menu and run the TRANSFRM program again.!! "#%& "#%& "#(%& )*+,--"./0/1)2( )*+,3--"./0/)2 )*+,4--"./0/) 25 )*+,3--"--"./0/1 /)2 6' 78 7 6'78 7 8 6'%78 %7 8% :# <=; >>)! 6!) <=; >(>)?,!<) <=;>>)!! ) <=; >5>)(,! <@ 9) <=; >>) 96 ":6:<9) <=;>A>)B@6 ) C (, ( 5 ;=# 88.8* ) < 9C) )9) )!) C )9<9: C) ) 9) )!) C ) 9 :.C) ) 9) )!) C% 6;-EF"A /. 6;-EFG"/* 6' EH85, 6'%D F-6;-EF +// F6;--EF(+//, ( 5 A G! A!G %&# 26
Clean-Up After you quit the program, you may want to go to the Y= screen and clear the functions so they don t interfere with future work. "!.0#/12"## To use the absolute-value function, press [OPTN] [F5] (NUM) [F1] (Abs). For example, to graph y = x - 3, enter Y1=abs(x - 3) into the Y= screen, set an appropriate window, and press [F6] (DRAW).! #3.# You can limit the domain of a function by graphing a function within a specific range of x values. When inputting the equation of a graph, you can specify a start point and an end point within brackets [ and ] separated by a comma. For example, if you want to graph y = 2 + x 2 on the interval [-1,10], you would enter Y1 = 2 + x 2, [-1,10] in the Graph Function menu. By specifying a domain for several different graphs, you can define a piecewise function that is defined over a limited domain. For example, enter the following into the Graph Function menu. Use the View Window [-4.7, 4.7, 1, -1, 7, 1]. Y1 = 4 + x, [-3,-1] Y2 = 2 + x 2, [-1,2]!+* #//- # The sketch function lets you draw lines and plot points on a graph that is already on the screen. In the following examples, the graph of Y1 = x(x + 2)(x 2) has already been graphed. Follow these steps to draw a segment: a. Press [SHIFT] [F4] (Sketch) [F6] [F2] [F2] (F-Line) 27
b. Arrow to one endpoint of the segment you want and press [EXE]. c. Arrow to the other endpoint and press [EXE] again. Repeat these steps beginning at an existing endpoint to sketch an enclosed figure. You can also draw segments by entering instructions in the RUN Mode. To draw a segment between (1, 3.64) and (7.4, 3.64), enter F-Line 1,3.64,7.4,3.64. To erase any drawing, press [SHIFT] [F4] (Sketch) [F1] [EXE]. 28