Chapter Graphing A collection of versatile graphing tools plus a large 127 × 63-dot display makes it easy to draw a variety of function graphs quickly and easily. This calculator is capable of drawing the following types of graphs. • Rectangular coordinate (Y =) graphs • Polar coordinate (r =) graphs • Parametric graphs • X = constant graphs • Inequality graphs • Integration graphs (in the RUN mode only) A selection of graph commands also makes it possible to incorporate graphing into programs.
8-1 Before Trying to Draw a Graph k Entering the Graph Mode On the Main Menu, select the GRAPH icon and enter the GRAPH Mode. When you do, the Graph Function menu appears on the display. You can use this menu to store, edit, and recall functions and to draw their graphs. Memory area Use f and c to change selection. • {SEL} ... {draw/non-draw status} • {DEL} ... {function delete} • {TYPE} ... {graph type menu} • {COLR} ... {graph color} CFX • {GMEM} ... {graph memory save/recall} • {DRAW} ...
8-2 View Window (V-Window) Settings Use the View Window to specify the range of the x-and y-axes, and to set the spacing between the increments on each axis. You should always set the View Window parameters you want to use before drawing a graph. 1. Press !3(V·Window) to display the View Window. X min ............ Minimum x-axis value X max ........... Maximum x-axis value X scale ......... Spacing of x-axis increments Y min ............ Minimum y-axis value Y max ........... Maximum y-axis value Y scale .
8-2 View Window (V-Window) Settings The nearby illustration shows the meaning of each of these parameters. min pitch (r, θ) or (X, Y ) max 3. To exit the View Window, press J or ! Q. • Pressing w without inputting any value also exits the View Window. • The following is the input range for View Window parameters. –9.9999E+97 to 9.99999E+97 • You can input parameter values up to 14 digits long.
View Window (V-Window) Settings 8-2 k Initializing and Standardizing the View Window uTo initialize the View Window You can use either of the following two methods to initialize the View Window. Normal initialization Press !3 (V-Window) 1 (INIT) to initialize the View Window to the following settings. Xmin = –6.3 Ymin = –3.1 Xmax = 6.3 Ymax = 3.1 Xscale = 1 Yscale = 1 Trigonometric initialization Press ! 3 (V-Window) 2 (TRIG) to initialize the View Window to the following settings.
8-2 View Window (V-Window) Settings k View Window Memory You can store up to six sets of View Window settings in View Window memory for recall when you need them. uTo store View Window settings Inputting View Window values and then pressing 4 (STO) 1 (V·W1) stores the View Window contents in View Window memory V·W1. • There are six View Window memories numbered V·W1 to V·W6. • Storing View Window settings in a memory area that already contains settings replaces the existing settings with the new ones.
8-3 Graph Function Operations You can store up to 20 functions in memory. Functions in memory can be edited, recalled, and graphed. k Specifying the Graph Type Before you can store a graph function in memory, you must first specify its graph type. 1. While the Graph Function Menu is on the display, press 3 (TYPE) to display the graph type menu, which contains the following items. • {Y=}/{r=}/{Parm}/{X=c} ... {rectangular coordinate}/{polar coordinate}/ {parametric}/{X=constant} graph s} ...
-3 Graph Function Operations uTo store a parametric function Example To store the following functions in memory areas Xt3 and Yt3 : x = 3 sin T y = 3 cos T 3(TYPE)3(Parm) (Specifies parametric expression.) dsvw(Inputs and stores x expression.) dcvw(Inputs and stores y expression.) • You will not be able to store the expression in an area that already contains a rectangular coordinate expression, polar coordinate expression, X = constant expression or inequality.
Graph Function Operations 8-3 k Editing Functions in Memory uTo edit a function in memory Example To change the expression in memory area Y1 from y = 2x2 – 5 to y = 2x2 – 3 e (Displays cursor.) eeeed(Changes contents.) w(Stores new graph function.) uTo delete a function 1. While the Graph Function Menu is on the display, press f or c to display the cursor and move the highlighting to the area that contains the function you want to delete. 2. Press 2 (DEL). 3.
8-3 Graph Function Operations uTo specify the draw/non-draw status of a graph Example To select the following functions for drawing : Y1 = 2x2 – 5 r2 = 5 sin3θ Use the following View Window parameters. Xmin = –5 Ymin = –5 Xmax = 5 Ymax = 5 Xscale = 1 Yscale = 1 cc (Select a memory area that contains a function for which you want to specify non-draw.) 1(SEL) (Specify non-draw.) Unhighlights cc1(SEL) c1(SEL) 6(DRAW) or w (Draws the graphs.
Graph Function Operations 8-3 • You can use the set up screen settings to alter the appearance of the graph screen as shown below. • Grid: On (Axes: On Label: Off) P.6 This setting causes dots to appear at the grid intersects on the display. • Axes: Off (Label: Off Grid: Off) This setting clears the axis lines from the display. • Label: On (Axes: On Grid: Off) This setting displays labels for the x- and y-axes.
Graph Function Operations 8-3 8-4 Graph Memory Graph memory lets you store up to six sets of graph function data and recall it later when you need it. A single save operation saves the following data in graph memory.
8-5 Drawing Graphs Manually After you select the RUN icon in the Main Menu and enter the RUN Mode, you can draw graphs manually. First press ! 4 (Sketch) 5 (GRPH) to recall the Graph Command Menu, and then input the graph function. • {Y=}/{r=}/{Parm}/{X=c}/{G∫dx} ... {rectangular coordinate}/{polar coordinate}/ {parametric}/{X = constant}/{integration} graph t}/{Ys s } ...
8-5 Drawing Graphs Manually uTo graph using polar coordinates (r =) [Sketch]-[GRPH]-[r=] You can graph functions that can be expressed in the format r = f (θ). To graph r = 2 sin3θ Example Use the following View Window parameters. = –2 T, θ min = 0 Xmax = 3 Ymax = 2 T, θ max = π Xscale = 1 Yscale = 1 T, θ pitch = π÷36 Xmin = –3 Ymin 1. In the set up screen, specify “r =” for Func Type. 2. Specify “Rad” as the angle unit and then press J. 3. Input the polar coordinate expression (r =).
Drawing Graphs Manually uTo graph parametric functions 8-5 [Sketch]-[GRPH]-[Parm] You can graph parametric functions that can be expressed in the following format. (X, Y) = ( f (T), g (T)) Example To graph the following parametric functions: x = 7 cos T – 2 cos 3.5T y = 7 sin T – 2 sin 3.5T Use the following View Window parameters. Xmin = –20 Ymin T, θ min = 0 = –12 Xmax = 20 Ymax = 12 T, θ max = 4π Xscale = Yscale = T, θ pitch = π÷36 5 5 1.
8-5 Drawing Graphs Manually 2. Input the expression. !4(Sketch)1(Cls)w 5(GRPH)4(X = c)d 3. Press w to draw the graph. [Sketch]-[GRPH]-[Y>]/[Y<]/[Y≥]/[Y≤] uTo graph inequalities You can graph inequalities that can be expressed in the following four formats. • y > f (x) Example • y < f (x) • y > f (x) • y < f (x) To graph the inequality y > x2 – 2x – 6 Use the following View Window parameters. Xmin = –6 Ymin = –10 Xmax = 6 Ymax = 10 Xscale = 1 Yscale = 5 1.
Drawing Graphs Manually uTo draw an integration graph 8-5 [Sketch]-[GRPH]-[G∫dx] You can graph an integration calculation performed using the function y = f(x). Example To graph the following, with a tolerance of “tol” = 1E - 4: ∫ 1 –2 (x + 2) (x – 1) (x – 3) dx Use the following View Window parameters. Xmin = –4 Ymin = –8 Xmax = 4 Ymax = 12 Xscale = 1 Yscale = 5 1. In the set up screen, specify “Y=” for Func Type and then press J . 2. Input the integration graph expression.
8-6 Other Graphing Functions The functions described in this section tell you how to read the x- and y-coordinates at a given point, and how to zoom in and zoom out on a graph. • These functions can be used with rectangular coordinate, polar coordinate, parametric, X = constant, and inequality graphs only. k Connect Type and Plot Type Graphs (Draw Type) P.5 You can use the Draw Type setting of the set up screen to specify one of two graph types.
Other Graphing Functions 8-6 1. After drawing the graphs, press 1 (Trace) to display the pointer in the center of the graph. • The pointer may not be visible on the graph when you press 1 (Trace). 2. Use d to move the pointer to the first intersection. d~d x / y coordinate values • Pressing d and e moves the pointer along the graph. Holding down either key moves the pointer at high speed. 3. Use f and c to move the pointer between the two graphs. 4. Use e to move the pointer to the other intersection.
8-6 Other Graphing Functions • The following shows how the display of coordinates and the derivative changes according to the Graph Type setting. • Rectangular Coordinate Graph • Polar Coordinate Graph • Parametric Function Graph • X = Constant Graph • Inequality Graph • The derivative is not displayed when you use trace with a built-in scientific function. P.6 • Setting the Coord item in the set up screen to “Off” turns display of the coordinates for the current pointer location off.
Other Graphing Functions 8-6 k Graphing in a Specific Range You can use the following syntax when inputting a graph to specify a start point and end point. , ! [ , ! ] w Example To graph y = x2 + 3x – 5 within the range of –2 < x < 4 Use the following View Window parameters. Xmin = –3 Ymin = –10 Xmax = 5 Ymax = 30 Xscale = 1 Yscale = 5 3(TYPE)1(Y =) (Specifies graph type.) vx+dv-f, ![-c,e!]w (Stores expression.) 6(DRAW) or w(Draws graph.
8-6 Other Graphing Functions 6(DRAW) (Draws graph.) ↓ ↓ • The function that is input using the above syntax can have only one variable. • You cannot use X, Y, r, θ, or T as the variable name. • You cannot assign a variable to the variable in the function. P.7 • When the set up screen’s Simul Graph item is set to “On”, the graphs for all the variables are drawn simultaneously. • You can use overwrite with rectangular coordinate, polar coordinate, parametric, and inequality graphs.
Other Graphing Functions uTo use box zoom 8-6 [Zoom]-[BOX] With box zoom, you draw a box on the display to specify a portion of the graph, and then enlarge the contents of the box. Example To use box zoom to enlarge a portion of the graph y = (x + 5) (x + 4) (x + 3) Use the following View Window parameters. Xmin = –8 Ymin = –4 Xmax = 8 Ymax = 2 Xscale = 2 Yscale = 1 1. After graphing the function, press 2 (Zoom). 1 2 3 4 5 6 2.
8-6 Other Graphing Functions • To return to the original graph, press 2 (Zoom) 6 (g) 1 (ORIG). • Nothing happens if you try to locate the second corner at the same location or directly above the first corner. • You can use box zoom for any type of graph. uTo use factor zoom [Zoom]-[FACT]-[IN]/[OUT] With factor zoom, you can zoom in or zoom out on the display, with the current pointer location being at the center of the new display. • Use the cursor keys to move the pointer around the display.
Other Graphing Functions 8-6 4. Press J to return to the graphs, and then press 3 (IN) to enlarge them. This enlarged screen makes it clear that the graphs of the two expressions are not tangential. Note that the above procedure can also be used to reduce the size of a graph (zoom out). In step 4, press 4 (OUT). • The above procedure automatically converts the x-range and y-range View Window values to 1/5 of their original settings.
8-6 Other Graphing Functions k Graph Range Adjustment Function [Zoom]-[SQR] This function makes the View Window x-range value the same as the y-range value. It is helpful when drawing circular graphs. Example To graph r = 5sin θ and then adjust the graph. Use the following View Window parameters. Xmin = –8 Ymin = –1 Xmax = 8 Ymax = 5 Xscale = 1 Yscale = 1 1. After drawing the graph, press 2 (Zoom) 6 (g). 1 2 3 4 5 6 2. Press 2 (SQR) to make the graph a circle.
Other Graphing Functions 8-6 2. Press 2 (Zoom) 6 (g). 3. Press 3 (RND) and then 1 (Trace). Use d to move the pointer to the other intersection. The rounded coordinate values for the pointer position appear on the screen. k Integer Function [Zoom]-[INTG] This function makes the dot width equal 1, converts axis values to integers, and redraws the graph.
8-6 Other Graphing Functions k Notes on the Auto View Window, Graph Range Adjustment, Coordinate Rounding, Integer, and Zoom Functions • These functions can be used with all graphs. • These functions cannot be incorporated into programs. • These functions can be used with a graph produced by a multi-statement connected by “ : ”, even if the multi-statement includes non-graph operations.
8-7 Picture Memory You can save up to six graphic image in picture memory for later recall. You can overdraw the graph on the screen with another graph stored in picture memory. uTo store a graph in picture memory Pressing K1(PICT)1(STO)1(Pic1) stores the graph drawn on the display in picture memory Pic1. • There are six picture memories numbered Pic1 to Pic6. • Storing a graph in a memory area that already contains data replaces the existing data with the new data.
8-8 Graph Background P.6 You can use the set up screen to specify the memory contents of any picture memory area (Pict 1 through Pict 6) as the Background item. When you do, the contents of the corresponding memory area is used as the background of the graph screen. • You can use a background in the RUN, STAT, GRAPH, DYNA, TABLE, RECUR, CONICS Modes.
Graph Background Example 2 8-8 With a statistical histogram as the background, graph a normal distribution Recall the backgound graph. (Histogram) Graph the normal distribution. P.249 • See “18. Statistical Graphs and Calculations” for details on drawing a statistical graphs.
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