# Casio ALGEBRA FX 2.0 PLUS Manual

Graphing

Graphing
Sections 5-1 and 5-2 of this chapter provide basic information
you need to know in order to draw a graph. The remaining
sections describe more advanced graphing features and functions.
Select the icon in the Main Menu that suits the type of graph you
want to draw or the type of table you want to generate.
·
• GRPH
TBL ... General function graphing or number table generation
• CONICS ... Conic section graphing
(5-1-5 ~ 5-1-6, 5-11-17~5-11-21)
·
• RUN
MAT ... Manual graphing (5-6-1 ~ 5-6-4)
• DYNA ... Dynamic Graph (5-8-1 ~ 5-8-6)
• RECUR ... Recursion graphing or number table generation
(5-9-1 ~ 5-9-8)
5-1
Sample Graphs
5-2
Controlling What Appears on a Graph Screen
5-3
Drawing a Graph
5-4
Storing a Graph in Picture Memory
5-5
Drawing Two Graphs on the Same Screen
5-6
Manual Graphing
5-7
Using Tables
5-8
Dynamic Graphing
5-9
Graphing a Recursion Formula
5-10 Changing the Appearance of a Graph
5-11 Function Analysis
Chapter
20011101
19990401
5

#### Summary of Contents for Casio ALGEBRA FX 2.0 PLUS

• Page 1 Chapter Graphing Sections 5-1 and 5-2 of this chapter provide basic information you need to know in order to draw a graph. The remaining sections describe more advanced graphing features and functions. Select the icon in the Main Menu that suits the type of graph you want to draw or the type of table you want to generate.
• ### Page 2: Sample Graphs

5-1-1 Sample Graphs 5-1 Sample Graphs k k k k k How to draw a simple graph (1) Description To draw a graph, simply input the applicable function. Set Up 1. From the Main Menu, enter the GRPH TBL Mode. •...
• Page 3 5-1-2 Sample Graphs ○ ○ ○ ○ ○ Example To graph Procedure 1 m GRPH • 2 dvxw 3 5(DRAW) (or w) Result Screen 19990401...
• Page 4 5-1-3 Sample Graphs k k k k k How to draw a simple graph (2) Description You can store up to 20 functions in memory and then select the one you want for graphing. Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
• Page 5 5-1-4 Sample Graphs ○ ○ ○ ○ ○ Example Input the functions shown below and draw their graphs 2 = 3sin2 θ Y1 = 2 – 3, Procedure 1 m GRPH • 2 3(TYPE)b(Y=)cvx-dw 3(TYPE)c(r=)dscvw 3 5(DRAW) Result Screen (Param) (INEQUA) (Plot) 19990401...
• Page 6 5-1-5 Sample Graphs k k k k k How to draw a simple graph (3) Description Use the following procedure to graph the function of a parabola, circle, ellipse, or hyperbola. Set Up 1. From the Main Menu, enter the CONICS Mode. Execution 2.
• Page 7 5-1-6 Sample Graphs ○ ○ ○ ○ ○ Example Graph the circle (X–1) + (Y–1) Procedure 1 m CONICS 2 ccccw 3 bwbwcw 4 6(DRAW) Result Screen (Parabola) (Ellipse) (Hyperbola) 19990401...
• ### Page 8: Controlling What Appears On A Graph Screen

5-2-1 Controlling What Appears on a Graph Screen 5-2 Controlling What Appears on a Graph Screen k k k k k V-Window (View Window) Settings Use the View Window to specify the range of the - and -axes, and to set the spacing between the increments on each axis.
• Page 9 5-2-2 Controlling What Appears on a Graph Screen u V-Window Setting Precautions • Inputting zero for T θ ptch causes an error. • Any illegal input (out of range value, negative sign without a value, etc.) causes an error. • An error occurs when Xmax is less than Xmin, or Ymax is less than Ymin. When T θ max is less than T θ...
• Page 10 5-2-3 Controlling What Appears on a Graph Screen k k k k k Initializing and Standardizing the V-Window u To initialize the V-Window 1. From the Main Menu, enter the GRPH TBL Mode. • 2. Press !K(V-Window). This displays the V-Window setting screen. 3.
• Page 11 5-2-4 Controlling What Appears on a Graph Screen k k k k k V-Window Memory You can store up to six sets of V-Window settings in V-Window memory for recall when you need them. u To store V-Window settings 1. From the Main Menu, enter the GRPH TBL Mode.
• Page 12 5-2-5 Controlling What Appears on a Graph Screen k k k k k Specifying the Graph Range Description You can define a range (start point, end point) for a function before graphing it. Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
• Page 13 5-2-6 Controlling What Appears on a Graph Screen ○ ○ ○ ○ ○ – 2 within the range – 2 < < 4 Example Graph Use the following V-Window settings. Xmin = –3, Xmax = 5, Xscale = 1 Ymin = –10, Ymax = 30, Yscale = 5 Procedure...
• Page 14 5-2-7 Controlling What Appears on a Graph Screen k k k k k Zoom Description This function lets you enlarge and reduce the graph on the screen. Set Up 1. Draw the graph. Execution 2. Specify the zoom type. 2(ZOOM)b(Box) ... Box zoom Draw a box around a display area, and that area is enlarged to fill the entire screen.
• Page 15 5-2-8 Controlling What Appears on a Graph Screen ○ ○ ○ ○ ○ Example Graph + 5)( + 4)( + 3), and then perform a box zoom. Use the following V-Window settings. Xmin = –8, Xmax = 8, Xscale = 2 Ymin = –...
• Page 16 5-2-9 Controlling What Appears on a Graph Screen k k k k k Factor Zoom Description With factor zoom, you can zoom in or out, centered on the current cursor position. Set Up 1. Draw the graph. Execution 2. Press 2(ZOOM)c(Factor) to open a pop-up window for specifying the -axis and -axis zoom factor.
• Page 17 5-2-10 Controlling What Appears on a Graph Screen ○ ○ ○ ○ ○ Example Enlarge the graphs of the two expressions shown below five times on both the -and -axis to see if they are tangent. Y1 = ( + 4)( + 1)( –...
• Page 18 5-2-11 Controlling What Appears on a Graph Screen k k k k k Turning Function Menu Display On and Off Press ua to toggle display of the menu at the bottom of the screen on and off. Turning off the function menu display makes it possible to view part of a graph hidden behind it.
• Page 19 5-2-12 Controlling What Appears on a Graph Screen k k k k k About the Calc Window Pressing u4(CAT/CAL) while a graph or number table is on the display opens the Calc Window. You can use the Calc Window to perform calculations with values obtained from graph analysis, or to change the value assigned to variable A in Y = AX and other expressions and then redraw the graph.
• ### Page 20: Drawing A Graph

5-3-1 Drawing a Graph 5-3 Drawing a Graph You can store up to 20 functions in memory. Functions in memory can be edited, recalled, and graphed. k k k k k Specifying the Graph Type Before you can store a graph function in memory, you must first specify its graph type. 1.
• Page 21 5-3-2 Drawing a Graph u To store a parametric function * ○ ○ ○ ○ ○ Example To store the following functions in memory areas Xt3 and Yt3 : = 3 sin T = 3 cos T 3(TYPE)d(Param) (Specifies parametric expression.) dsvw(Inputs and stores expression.) dcvw(Inputs and stores...
• Page 22 5-3-3 Drawing a Graph u To create a composite function ○ ○ ○ ○ ○ Example To register the following functions as a composite function: Y1= (X + 1), Y2 = X Assign Y1 ° Y2 to Y3, and Y2 ° Y1 to Y4. (Y1 °...
• Page 23 5-3-4 Drawing a Graph ffffi1(SEL)5(DRAW) The above three screens are produced using the Trace function. See “5-11 Function Analysis” for more information. • If you do not specify a variable name (variable A in the above key operation), the calculator automatically uses one of the default variables listed below.
• Page 24 5-3-5 Drawing a Graph k k k k k Editing and Deleting Functions u To edit a function in memory ○ ○ ○ ○ ○ Example To change the expression in memory area Y1 from – 5 to – 3 e (Displays cursor.) eeeeDd(Changes contents.) w(Stores new graph function.)
• Page 25 5-3-6 Drawing a Graph k k k k k Selecting Functions for Graphing u To specify the draw/non-draw status of a graph ○ ○ ○ ○ ○ Example To select the following functions for drawing : 2 = 5 sin3 θ Y1 = 2 –...
• Page 26 5-3-7 Drawing a Graph k k k k k Graph Memory Graph memory lets you store up to 20 sets of graph function data and recall it later when you need it. A single save operation saves the following data in graph memory. •...
• ### Page 27: Storing A Graph In Picture Memory

5-4-1 Storing a Graph in Picture Memory 5-4 Storing a Graph in Picture Memory You can save up to 20 graphic images in picture memory for later recall. You can overdraw the graph on the screen with another graph stored in picture memory. u To store a graph in picture memory TBL Mode, press 6(g)1(PICT)b(Store) to display the 1.
• ### Page 28: Drawing Two Graphs On The Same Screen

5-5-1 Drawing Two Graphs on the Same Screen 5-5 Drawing Two Graphs on the Same Screen k k k k k Copying the Graph to the Sub-screen Description Dual Graph lets you split the screen into two parts. Then you can graph two different functions in each for comparison, or draw a normal size graph on one side and its enlarged version on the other side.
• Page 29 5-5-2 Drawing Two Graphs on the Same Screen ○ ○ ○ ○ ○ Example Graph + 1)( – 1) in the main screen and sub-screen. Use the following V-Window settings. (Main Screen) Xmin = –2, Xmax = 2, Xscale = 0.5 Ymin = –2, Ymax = 2, Yscale = 1...
• Page 30 5-5-3 Drawing Two Graphs on the Same Screen k k k k k Graphing Two Different Functions Description Use the following procedure to graph different functions in the main screen and sub-screen. Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
• Page 31 5-5-4 Drawing Two Graphs on the Same Screen ○ ○ ○ ○ ○ Example Graph + 1)( – 1) in the main screen, and – 3 in the sub- screen. Use the following V-Window settings. (Main Screen) Xmin = –4, Xmax = 4, Xscale = 1 Ymin = –5,...
• Page 32 5-5-5 Drawing Two Graphs on the Same Screen k k k k k Using Zoom to Enlarge the Sub-screen Description Use the following procedure to enlarge the main screen graph and then move it to the sub- screen. Set Up 1.
• Page 33 5-5-6 Drawing Two Graphs on the Same Screen ○ ○ ○ ○ ○ Example Draw the graph + 1)( – 1) in the main screen, and then use Box Zoom to enlarge it. Use the following V-Window settings. (Main Screen) Xmin = –2, Xmax = 2, Xscale = 0.5...
• ### Page 34: Manual Graphing

5-6-1 Manual Graphing 5-6 Manual Graphing k k k k k Rectangular Coordinate Graph Description Inputting the Graph command in the RUN MAT Mode enables drawing of rectangular • coordinate graphs. Set Up 1. From the Main Menu, enter the RUN MAT Mode.
• Page 35 5-6-2 Manual Graphing ○ ○ ○ ○ ○ Example Graph – 4 Use the following V-Window settings. Xmin = –5, Xmax = 5, Xscale = 2 Ymin = –10, Ymax = 10, Yscale = 5 Procedure 1 m RUN • 2 !K(V-Window) -fwfwcwc -bawbawfwi 3 K6(g)6(g)2(SKTCH)b(Cls)w...
• Page 36 5-6-3 Manual Graphing k k k k k Integration Graph Description Inputting the Graph command in the RUN MAT Mode enables graphing of functions • produced by an integration calculation. The calculation result is shown in the lower left of the display, and the calculation range is blackened in the graph.
• Page 37 5-6-4 Manual Graphing ○ ○ ○ ○ ○ ∫ Example Graph the integration + 2)( – 1)( – 3) dx. –2 Use the following V-Window settings. Xmin = –4, Xmax = 4, Xscale = 1 Ymin = –8, Ymax = 12, Yscale = 5 Procedure 1 m RUN...
• Page 38 5-6-5 Manual Graphing k k k k k Drawing Multiple Graphs on the Same Screen Description Use the following procedure to assign various values to a variable contained in an expres- sion and overwrite the resulting graphs on the screen. Set Up 1.
• Page 39 5-6-6 Manual Graphing ○ ○ ○ ○ ○ Example To graph – 3 as the value of A changes in the sequence 3, 1, –1. Use the following V-Window settings. Xmin = –5, Xmax = 5, Xscale = 1 Ymin = –10, Ymax = 10, Yscale = 2 Procedure...
• ### Page 40: Using Tables

5-7-1 Using Tables 5-7 Using Tables k k k k k Storing a Function and Generating a Number Table u To store a function ○ ○ ○ ○ ○ Example To store the function – 2 in memory area Y1 Use f and c to move the highlighting in the Graph function list to the memory area where you want to store the function.
• Page 41 5-7-2 Using Tables u To generate a table using a list 1. While the Graph function list is on the screen, display the SET UP screen. 2. Highlight Variable and then press 2(LIST) to display the pop-up window. 3. Select the list whose values you want to assign for the x-variable. •...
• ### Page 42: Specifying The Function Type

5-7-3 Using Tables You can use cursor keys to move the highlighting around the table for the following purposes. • To display the selected cell’s value at the bottom of the screen, using the calculator’s current number of decimal place, number of significant digit, and exponential display range settings •...
• Page 43 5-7-4 Using Tables k k k k k Editing and Deleting Functions u To edit a function ○ ○ ○ ○ ○ Example To change the function in memory area Y1 from – 2 to – 5 Use f and c to move the highlighting to the function you want to edit. Use d and e to move the cursor to the location of the change.
• Page 44 5-7-5 Using Tables k k k k k Editing Tables You can use the table menu to perform any of the following operations once you generate a table. • Change the values of variable • Edit (delete, insert, and append) rows •...
• Page 45 5-7-6 Using Tables Row Operations u To delete a row ○ ○ ○ ○ ○ Example To delete Row 2 of the table generated on page 5-7-2 6(g)1(R·DEL) u To insert a row ○ ○ ○ ○ ○ Example To insert a new row between Rows 1 and 2 in the table generated on page 5-7-2 6(g)2(R·INS) 19990401...
• Page 46 5-7-7 Using Tables u To add a row ○ ○ ○ ○ ○ Example To add a new row below Row 7 in the table generated on page 5-7-2 6(g)3(R·ADD) cccccc Deleting a Table 1. Display the table and then press 2(DEL·A). 2.
• Page 47 5-7-8 Using Tables k k k k k Copying a Table Column to a List A simple operation lets you copy the contents of a numeric table column into a list. u To copy a table to a list ○ ○ ○ ○ ○ Example To copy the contents of Column into List 1...
• Page 48 5-7-9 Using Tables k k k k k Drawing a Graph from a Number Table Description Use the following procedure to generate a number table and then draw a graph based on the values in the table. Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
• Page 49 5-7-10 Using Tables ○ ○ ○ ○ ○ Example Store the two functions below, generate a number table, and then draw a line graph. Specify a range of –3 to 3, and an increment of 1. Y1 = 3 – 2, Y2 = Use the following V-Window settings.
• Page 50 5-7-11 Using Tables k k k k k Specifying a Range for Number Table Generation Description Use the following procedure to specify a number table range when calculating scatter data from a function. Set Up 1. From the Main Menu, enter the GRPH TBL Mode.
• Page 51 5-7-12 Using Tables ○ ○ ○ ○ ○ Example Store the three functions shown below, and then generate a table for functions Y1 and Y3. Specify a range of –3 to 3, and an increment of 1. Y1 = 3 –...
• Page 52 5-7-13 Using Tables k k k k k Simultaneously Displaying a Number Table and Graph Description Specifying T+G for Dual Screen on the SET UP makes it possible to display a number table and graph at the same time. Set Up 1.
• Page 53 5-7-14 Using Tables ○ ○ ○ ○ ○ Example Store the function Y1 = 3 – 2 and simultaneously display its number table and line graph. Use a table range of –3 to 3 with an increment of 1. Use the following V-Window settings. Xmin = 0, Xmax = 6, Xscale = 1...
• Page 54 5-7-15 Using Tables k k k k k Using Graph-Table Linking Description With Dual Graph, you can use the following procedure to link the graph and table screens so the pointer on the graph screen jumps to the location of the currently selected table value. Set Up 1.
• Page 55 5-7-16 Using Tables ○ ○ ○ ○ ○ Example Store the function Y1 = 3log and simultaneously display its number table and plot-type graph. Use a table range of 2 through 9, with an increment of 1. Use the following V-Window settings. Xmin = –1, Xmax = 10, Xscale = 1...
• ### Page 56: Dynamic Graphing

5-8-1 Dynamic Graphing 5-8 Dynamic Graphing k k k k k Using Dynamic Graph Description Dynamic Graph lets you define a range of values for the coefficients in a function, and then observe how a graph is affected by changes in the value of a coefficient. It helps to see how the coefficients and terms that make up a function influence the shape and position of a graph.
• Page 57 5-8-2 Dynamic Graphing ○ ○ ○ ○ ○ Example Use Dynamic Graph to graph = A ( – 1) – 1, in which the value of coefficient A changes from 2 through 5 in increments of 1. The Graph is drawn 10 times. Use the following V-Window settings.
• Page 58 5-8-3 Dynamic Graphing k k k k k Dynamic Graph Application Examples Description You can also use Dynamic Graph to simulate simple physical phenomena. Set Up 1. From the Main Menu, enter the DYNA Mode. 2. Make V-Window settings. Execution 3.
• Page 59 5-8-4 Dynamic Graphing ○ ○ ○ ○ ○ Example The path over time T of a ball thrown in the air at initial velocity V and an angle of θ degrees from horizontal can be calculated as follows. X = (Vcos θ ) T, Y = (Vsin θ ) T – (1/2)gT (g = 9.8m/s Use Dynamic Graph to plot the path of a ball thrown at an initial velocity of 20 meters per second, at horizontal angles of 30, 45, and 60...
• Page 60 5-8-5 Dynamic Graphing k Adjusting the Dynamic Graph Speed You can use the following procedure to adjust the Dynamic Graph speed while the draw operation is taking place. 1. While a Dynamic Graph draw operation is being performed, press A to change to the speed adjustment menu.
• Page 61 5-8-6 Dynamic Graphing k k k k k Using Dynamic Graph Memory You can store Dynamic Graph conditions and screen data in Dynamic Graph memory for later recall when you need it. This lets you save time, because you can recall the data and immediately begin a Dynamic Graph draw operation.
• ### Page 62: Graphing A Recursion Formula

5-9-1 Graphing a Recursion Formula 5-9 Graphing a Recursion Formula k k k k k Generating a Number Table from a Recursion Formula Description You can input up to three of the following types of recursion formulas and generate a number table.
• Page 63 5-9-2 Graphing a Recursion Formula ○ ○ ○ ○ ○ Example Generate a number table from recursion between three terms as expressed by , with initial terms of = 1, (Fibonacci sequence), as changes in value from 1 to 6. Procedure 1 m RECUR 2 3(TYPE)d(...
• Page 64 5-9-3 Graphing a Recursion Formula k k k k k Graphing a Recursion Formula (1) Description After generating a number table from a recursion formula, you can graph the values on a line graph or plot type graph. Set Up 1.
• Page 65 5-9-4 Graphing a Recursion Formula ○ ○ ○ ○ ○ Example Generate a number table from recursion between two terms as expressed by +1, with an initial term of = 1, as changes in value from 1 to 6. Use the table values to draw a line graph. Use the following V-Window settings.
• Page 66 5-9-5 Graphing a Recursion Formula k k k k k Graphing a Recursion Formula (2) Description The following describes how to generate a number table from a recursion formula and graph the values while Σ Display is On. Set Up 1.
• Page 67 5-9-6 Graphing a Recursion Formula ○ ○ ○ ○ ○ Example Generate a number table from recursion between two terms as expressed by +1, with an initial term of = 1, as changes in value from 1 to 6. Use the table values to draw a plot line graph with ordinate Σ...
• Page 68 5-9-7 Graphing a Recursion Formula k k k k k WEB Graph (Convergence, Divergence) Description ) is graphed by presuming for linear two-term regression composed of . Next, it can be determined whether the function is convergent or divergent. Set Up 1.
• Page 69 5-9-8 Graphing a Recursion Formula ○ ○ ○ ○ ○ Example To draw the WEB graph for the recursion formula = –3( + 0.2, and check for divergence or convergence. Use the following table range and V-Window Settings. Table Range Start = 0, End = 6, = 0.01, Str = 0.01,...
• ### Page 70: Changing The Appearance Of A Graph

5-10-1 Changing the Appearance of a Graph 5-10 Changing the Appearance of a Graph k k k k k Drawing a Line Description The sketch function lets you draw points and lines inside of graphs. Set Up 1. Draw the graph. Execution 2.
• Page 71 5-10-2 Changing the Appearance of a Graph ○ ○ ○ ○ ○ Example Draw a line that is tangent to point (2, 0) on the graph for + 2)( – 2). Use the following V-Window settings. Xmin = –5, Xmax = 5, Xscale = 1 Ymin = –5, Ymax = 5,...
• Page 72 5-10-3 Changing the Appearance of a Graph k k k k k Inserting Comments Description You can insert comments anywhere you want in a graph. Set Up 1. Draw the graph. Execution 2. Press 3(SKTCH)e(Text), and a pointer appears in the center of the display. 3.
• Page 73 5-10-4 Changing the Appearance of a Graph ○ ○ ○ ○ ○ Example Insert text into the graph + 2)( – 2). Use the following V-Window settings. Xmin = –5, Xmax = 5, Xscale = 1 Ymin = –5, Ymax = 5, Yscale = 1 Procedure 1 m GRPH...
• Page 74 5-10-5 Changing the Appearance of a Graph k k k k k Freehand Drawing Description You can use the pen option for freehand drawing in a graph. Set Up 1. Draw the graph. Execution 2. Press 3(SKTCH)f(Pen), and a pointer appears in the center of the screen. 3.
• Page 75 5-10-6 Changing the Appearance of a Graph ○ ○ ○ ○ ○ Example Use the pen to draw on the graph + 2)( – 2). Use the following V-Window settings. Xmin = –5, Xmax = 5, Xscale = 1 Ymin = –5, Ymax = 5, Yscale = 1 Procedure...
• Page 76 5-10-7 Changing the Appearance of a Graph k k k k k Changing the Graph Background You can use the set up screen to specify the memory contents of any picture memory area (Pict 1 through Pict 20) as the Background item. When you do, the contents of the corresponding memory area is used as the background of the graph screen.
• Page 77 5-10-8 Changing the Appearance of a Graph Draw the dynamic graph. (Y = X – 1) ↓↑ (Y = X ↓↑ (Y = X + 1) • See “5-8-1 Dynamic Graphing” for details on using the Dynamic Graph feature. 19990401...
• ### Page 78: Function Analysis

5-11-1 Function Analysis 5-11 Function Analysis k k k k k Reading Coordinates on a Graph Line Description Trace lets you move a pointer along a graph and read out coordinates on the display. Set Up 1. Draw the graph. Execution 2.
• Page 79 5-11-2 Function Analysis ○ ○ ○ ○ ○ Example Read coordinates along the graph of the function shown below. Y1 = – 3 Use the following V-Window settings. Xmin = –5, Xmax = 5, Xscale = 1 Ymin = –10, Ymax = 10, Yscale = 2 Procedure...
• Page 80 5-11-3 Function Analysis k k k k k Displaying the Derivative Description In addition to using Trace to display coordinates, you can also display the derivative at the current pointer location. Set Up 1. On the SET UP screen, specify On for Derivative. 2.
• Page 81 5-11-4 Function Analysis ○ ○ ○ ○ ○ Example Read coordinates and derivatives along the graph of the function shown below. Y1 = – 3 Use the following V-Window settings. Xmin = –5, Xmax = 5, Xscale = 1 Ymin = –10, Ymax = 10, Yscale = 2 Procedure...
• Page 82 5-11-5 Function Analysis k k k k k Graph to Table Description You can use trace to read the coordinates of a graph and store them in a number table. You can also use Dual Graph to simultaneously store the graph and number table, making this an important graph analysis tool.
• Page 83 5-11-6 Function Analysis ○ ○ ○ ○ ○ Example Save, in a table, the coordinates in the vicinity of the points of intersection at X = 0 for the two graphs shown below, and store the table contents in List 1. Y1 = –...
• Page 84 5-11-7 Function Analysis k k k k k Coordinate Rounding Description This function rounds off coordinate values displayed by Trace. Set Up 1. Draw the graph. Execution 2. Press 2(ZOOM)i(Rnd). This causes the V-Window settings to be changed automatically in accordance with the Rnd value. 3.
• Page 85 5-11-8 Function Analysis ○ ○ ○ ○ ○ Example Use coordinate rounding and display the coordinates in the vicinity of the points of intersection for the two graphs produced by the functions shown below. Y1 = – 3, Y2 = – Use the following V-Window settings.
• Page 86 5-11-9 Function Analysis k k k k k Calculating the Root Description This feature provides a number of different methods for analyzing graphs. Set Up 1. Draw the graphs. Execution 2. Select the analysis function. 4(G-SLV) b(Root) ... Calculation of root c(Max) ...
• Page 87 5-11-10 Function Analysis ○ ○ ○ ○ ○ Example Draw the graph shown below and calculate the root for Y1. Y1 = + 2)( – 2) Use the following V-Window settings. Xmin = –6.3, Xmax = 6.3, Xscale = 1 Ymin = –3.1, Ymax = 3.1, Yscale = 1 (initial defaults) Procedure 1 m GRPH...
• Page 88 5-11-11 Function Analysis k k k k k Calculating the Point of Intersection of Two Graphs Description Use the following procedure to calculate the point of intersection of two graphs. Set Up 1. Draw the graphs. Execution 2. Press 4(G-SLV)5(Isect). When there are three or more graphs, the selection cursor (k) appears at the lowest numbered graph.
• Page 89 5-11-12 Function Analysis ○ ○ ○ ○ ○ Example Graph the two functions shown below, and determine the point of intersection between Y1 and Y2. Y1 = + 1, Y2 = Use the following V-Window settings. Xmin = –5, Xmax = 5, Xscale = 1 Ymin = –5, Ymax = 5,...
• Page 90 5-11-13 Function Analysis k Determining the Coordinates for Given Points Description The following procedure describes how to determine the -coordinate for a given , and the -coordinate for a given Set Up 1. Draw the graph. Execution 2. Select the function you want to perform. When there are multiple graphs, the selection cursor (k) appears at the lowest numbered graph.
• Page 91 5-11-14 Function Analysis ○ ○ ○ ○ ○ Example Graph the two functions shown below and then determine the coordinate for = 0.5 and the -coordinate for = 2.2 on graph Y2. Y1 = + 1, Y2 = + 2)( –...
• Page 92 5-11-15 Function Analysis k k k k k Calculating the lntegral Value for a Given Range Description Use the following procedure to obtain integration values for a given range. Set Up 1. Draw the graph. Execution ∫dx 2. Press 4(G-SLV)i( ).
• Page 93 5-11-16 Function Analysis ○ ○ ○ ○ ○ Example Graph the function shown below, and then determine the integral value at (–2, 0). Y1 = + 2)( – 2) Use the following V-Window settings. Xmin = –6.3, Xmax = 6.3, Xscale = 1 Ymin = –4, Ymax = 4, Yscale = 1...
• Page 94 5-11-17 Function Analysis k k k k k Conic Section Graph Analysis You can determine approximations of the following analytical results using conic section graphs. • Focus/vertex/eccentricity • Latus rectum • Center/radius • -intercept • Directrix/axis of symmetry drawing and analysis •...
• Page 95 5-11-18 Function Analysis u To calculate the focus, vertex and latus rectum [G-SLV]-[Focus]/[Vertex]/[Length] ○ ○ ○ ○ ○ Example To determine the focus, vertex and latus rectum for the parabola X = (Y – 2) Use the following V-Window settings. Xmin = –1, Xmax = 10, Xscale = 1...
• Page 96 5-11-19 Function Analysis u To calculate the center and radius [G-SLV]-[Center]/[Radius] ○ ○ ○ ○ ○ Example To determine the center and radius for the circle (X + 2) + (Y + 1) Use the following V-Window settings. Xmin = –6.3, Xmax = 6.3, Xscale = 1 Ymin = –3.1, Ymax = 3.1, Yscale = 1 4(G-SLV) b(Center)
• Page 97 5-11-20 Function Analysis 4(G-SLV) h(Y-Icpt) (Calculates the -intercept.) • Press e to calculate the second set of -intercepts. Pressing d returns to the first set of intercepts. u To draw and analyze the axis of symmetry and directrix [G-SLV]-[Sym]/[Dirtrx] ○ ○ ○ ○ ○ Example To draw the axis of symmetry and directrix for the parabola X = 2(Y –...
• Page 98 5-11-21 Function Analysis To draw and analyze the asymptotes [G-SLV]-[Asympt] ○ ○ ○ ○ ○ Example To draw the asymptotes for the hyperbola (X – 1) (Y – 1) –––––––– – –––––––– = 1 Use the following V-Window settings. Xmin = –6.3, Xmax = 6.3, Xscale = 1 Ymin = –5, Ymax = 5, Yscale = 1...

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