Casio ALGEBRA FX 2.0 PLUS Graphing Instrukcja Użytkownika

19990401GraphingSections 5-1 and 5-2 of this chapter provide basic informationyou need to know in order to draw a graph. The remainingsections describ

19990401kkkkk Initializing and Standardizing the V-Windowu To initialize the V-Window1. From the Main Menu, enter the GRPH • TBL Mode.2. Press !K(V-Wi

19990401kkkkk V-Window MemoryYou can store up to six sets of V-Window settings in V-Window memory for recall when youneed them.u To s t ore V-Window s

19990401kkkkk Specifying the Graph RangeDescriptionYou can define a range (start point, end point) for a function before graphing it.Set Up1. From the

199904015-2-6Controlling What Appears on a Graph ScreenExample Graph y = x2 + 3x – 2 within the range – 2 < x < 4Use the following V-Window sett

199904015-2-7Controlling What Appears on a Graph Screenkkkkk ZoomDescriptionThis function lets you enlarge and reduce the graph on the screen.Set Up1.

199904015-2-8Controlling What Appears on a Graph Screen#You must specify two different points for boxzoom, and the two points cannot be on a straightl

199904015-2-9Controlling What Appears on a Graph Screenkkkkk Factor ZoomDescriptionWith factor zoom, you can zoom in or out, centered on the current c

199904015-2-10Controlling What Appears on a Graph ScreenExample Enlarge the graphs of the two expressions shown below five times onboth the x-and y-ax

19990401kkkkk Turning Function Menu Display On and OffPress ua to toggle display of the menu at the bottom of the screen on and off.Turning off the fu

19990401kkkkk About the Calc WindowPressing u4(CAT/CAL) while a graph or number table is on the display opens the CalcWindow. You can use the Calc Win

199904015-1-1Sample Graphs5-1 Sample Graphskkkkk How to draw a simple graph (1)DescriptionTo draw a graph, simply input the applicable function.Set Up

199904015-3-1Drawing a Graph5-3 Drawing a GraphYou can store up to 20 functions in memory. Functions in memory can be edited, recalled,and graphed.kkk

199904015-3-2Drawing a Graphu To store a parametric function *1Example To store the following functions in memory areas Xt3 and Yt3 :x = 3 sin Ty = 3

199904015-3-3Drawing a Graphu To c r eate a composite functionExample To register the following functions as a composite function:Y1= (X + 1), Y2 =

19990401ffffi1(SEL)5(DRAW)The above three screens are produced using the Trace function.See “5-11 Function Analysis” for more information.• If you do

1999040120011101kkkkk Editing and Deleting Functionsu To e d it a function in memoryExample To change the expression in memory area Y1 from y = 2x2 –

1999040120011101kkkkk Selecting Functions for Graphingu To specify the draw/non-draw status of a graphExample To select the following functions for dr

1999040120010102kkkkk Graph MemoryGraph memory lets you store up to 20 sets of graph function data and recall it later when youneed it.A single save o

199904015-4 Storing a Graph in Picture MemoryYou can save up to 20 graphic images in picture memory for later recall. You can overdrawthe graph on the

199904015-5 Drawing Two Graphs on the Same Screenkkkkk Copying the Graph to the Sub-screenDescriptionDual Graph lets you split the screen into two par

19990401Example Graph y = x(x + 1)(x – 1) in the main screen and sub-screen.Use the following V-Window settings.(Main Screen)Xmin = –2, Xmax = 2, Xsca

199904015-1-2Sample GraphsExample To graph y = 3x2Procedure1 m GRPH • TBL2dvxw3 5(DRAW) (or w)Result Screen

19990401kkkkk Graphing Two Different FunctionsDescriptionUse the following procedure to graph different functions in the main screen and sub-screen.Se

19990401Example Graph y = x(x + 1)(x – 1) in the main screen, and y = 2x2 – 3 in the sub-screen.Use the following V-Window settings.(Main Screen)Xmin

19990401kkkkk Using Zoom to Enlarge the Sub-screenDescriptionUse the following procedure to enlarge the main screen graph and then move it to the sub-

19990401Example Draw the graph y = x(x + 1)(x – 1) in the main screen, and then useBox Zoom to enlarge it.Use the following V-Window settings.(Main S

199904015-6-1Manual Graphing5-6 Manual Graphingkkkkk Rectangular Coordinate GraphDescriptionInputting the Graph command in the RUN • MAT Mode enables

199904015-6-2Manual GraphingExample Graph y = 2x2 + 3x – 4Use the following V-Window settings.Xmin = –5, Xmax = 5, Xscale = 2Ymin = –10, Ymax = 10, Ys

199904015-6-3Manual Graphingkkkkk Integration GraphDescriptionInputting the Graph command in the RUN • MAT Mode enables graphing of functionsproduced

199904015-6-4Manual GraphingExample Graph the integration ∫ (x + 2)(x – 1)(x – 3) dx.Use the following V-Window settings.Xmin = –4, Xmax = 4, Xscale

199904015-6-5Manual Graphingkkkkk Drawing Multiple Graphs on the Same ScreenDescriptionUse the following procedure to assign various values to a varia

199904015-6-6Manual GraphingExample To graph y = Ax2 – 3 as the value of A changes in the sequence 3, 1,–1.Use the following V-Window settings.Xmin =

199904015-1-3Sample Graphskkkkk How to draw a simple graph (2)DescriptionYou can store up to 20 functions in memory and then select the one you want f

199904015-7 Using Tableskkkkk Storing a Function and Generating a Number Tableu To s t ore a functionExample To store the function y = 3x2 – 2 in memo

19990401u To generate a table using a list1. While the Graph function list is on the screen, display the SET UP screen.2. Highlight Variable and then

19990401You can use cursor keys to move the highlighting around the table for the following purposes.•To display the selected cell’s value at the bott

19990401kkkkk Editing and Deleting Functionsu To e d it a functionExample To change the function in memory area Y1 from y = 3x2 – 2 toy = 3x2 – 5Use f

199904015-7-5Using Tableskkkkk Editing TablesYou can use the table menu to perform any of the following operations once you generate atable.•Change th

199904015-7-6Using TablesuRow Operationsu To delete a rowExample To delete Row 2 of the table generated on page 5-7-2c 6(g)1(R·DEL)u To insert a rowE

199904015-7-7Using Tablesu To a d d a rowExample To add a new row below Row 7 in the table generated on page 5-7-2cccccc 6(g)3(R·ADD)uDeleting a Table

19990401kkkkk Copying a Table Column to a ListA simple operation lets you copy the contents of a numeric table column into a list.u To copy a table t

19990401kkkkk Drawing a Graph from a Number TableDescriptionUse the following procedure to generate a number table and then draw a graph based on thev

19990401Example Store the two functions below, generate a number table, and then drawa line graph. Specify a range of –3 to 3, and an increment of 1.

199904015-1-4Sample GraphsExample Input the functions shown below and draw their graphsY1 = 2x2 – 3, r2 = 3sin2θProcedure1 m GRPH • TBL2 3(TYPE)b(Y=)c

19990401kkkkk Specifying a Range for Number Table GenerationDescriptionUse the following procedure to specify a number table range when calculating sc

19990401Example Store the three functions shown below, and then generate a table forfunctions Y1 and Y3. Specify a range of –3 to 3, and an increment

19990401kkkkk Simultaneously Displaying a Number Table and GraphDescriptionSpecifying T+G for Dual Screen on the SET UP makes it possible to display a

19990401Example Store the function Y1 = 3x2 – 2 and simultaneously display its numbertable and line graph. Use a table range of –3 to 3 with an increm

199904015-7-15Using Tableskkkkk Using Graph-Table LinkingDescriptionWith Dual Graph, you can use the following procedure to link the graph and table s

199904015-7-16Using TablesExample Store the function Y1 = 3logx and simultaneously display its numbertable and plot-type graph. Use a table range of 2

199904015-8 Dynamic Graphingkkkkk Using Dynamic GraphDescriptionDynamic Graph lets you define a range of values for the coefficients in a function, an

19990401Example Use Dynamic Graph to graph y = A (x – 1)2 – 1, in which the value ofcoefficient A changes from 2 through 5 in increments of 1. The Gra

19990401kkkkk Dynamic Graph Application ExamplesDescriptionYou can also use Dynamic Graph to simulate simple physical phenomena.Set Up1. From the Main

19990401Example The path over time T of a ball thrown in the air at initial velocity V andan angle of θ degrees from horizontal can be calculated as f

199904015-1-5Sample Graphskkkkk How to draw a simple graph (3)DescriptionUse the following procedure to graph the function of a parabola, circle, elli

19990401k Adjusting the Dynamic Graph SpeedYou can use the following procedure to adjust the Dynamic Graph speed while the drawoperation is taking pla

19990401kkkkk Using Dynamic Graph MemoryYou can store Dynamic Graph conditions and screen data in Dynamic Graph memory forlater recall when you need i

199904015-9 Graphing a Recursion Formulakkkkk Generating a Number Table from a Recursion FormulaDescriptionYou can input up to three of the following

19990401Example Generate a number table from recursion between three terms asexpressed by an +2 = an+1 + an, with initial terms of a1 = 1, a2 = 1(Fibo

19990401kkkkk Graphing a Recursion Formula (1)DescriptionAfter generating a number table from a recursion formula, you can graph the values on a lineg

19990401Example Generate a number table from recursion between two terms asexpressed by an+1 = 2an+1, with an initial term of a1 = 1, as n changesin v

19990401kkkkk Graphing a Recursion Formula (2)DescriptionThe following describes how to generate a number table from a recursion formula and graphthe

19990401Example Generate a number table from recursion between two terms asexpressed by an+1 = 2an+1, with an initial term of a1 = 1, as n changesin v

19990401kkkkk WEB Graph (Convergence, Divergence)Descriptiony = f(x) is graphed by presuming an+1 = y, an = x for linear two-term regression an+1 = f

19990401Example To draw the WEB graph for the recursion formula an+1 = –3(an)2 + 3an,bn +1 = 3bn + 0.2, and check for divergence or convergence. Use t

199904015-1-6Sample GraphsExample Graph the circle (X–1)2 + (Y–1)2 = 22Procedure1 m CONICS2 ccccw3bwbwcw4 6(DRAW)Result Screen(Parabola) (Ellipse) (Hy

199904015-10-1Changing the Appearance of a Graph5-10 Changing the Appearance of a Graphkkkkk Drawing a LineDescriptionThe sketch function lets you dra

19990401Example Draw a line that is tangent to point (2, 0) on the graph fory = x (x + 2)(x – 2).Use the following V-Window settings.Xmin = –5, Xmax =

19990401kkkkk Inserting CommentsDescriptionYou can insert comments anywhere you want in a graph.Set Up1. Draw the graph.Execution2. Press 3(SKTCH)e(Te

19990401Example Insert text into the graph y = x (x + 2)(x – 2).Use the following V-Window settings.Xmin = –5, Xmax = 5, Xscale = 1Ymin = –5, Ymax = 5

19990401kkkkk Freehand DrawingDescriptionYou can use the pen option for freehand drawing in a graph.Set Up1. Draw the graph.Execution2. Press 3(SKTCH)

19990401Example Use the pen to draw on the graph y = x (x + 2)(x – 2).Use the following V-Window settings.Xmin = –5, Xmax = 5, Xscale = 1Ymin = –5, Ym

199904015-10-7Changing the Appearance of a Graphkkkkk Changing the Graph BackgroundYou can use the set up screen to specify the memory contents of any

199904015-10-8Changing the Appearance of a GraphDraw the dynamic graph.(Y = X2 – 1)↓↑(Y = X2)↓↑(Y = X2 + 1)•See “5-8-1 Dynamic Graphing” for details o

199904015-11 Function Analysiskkkkk Reading Coordinates on a Graph LineDescriptionTrace lets you move a pointer along a graph and read out coordinates

19990401Example Read coordinates along the graph of the function shown below.Y1 = x2 – 3Use the following V-Window settings.Xmin = –5, Xmax = 5, Xscal

199904015-2 Controlling What Appears on a Graph Screenkkkkk V-Window (View Window) SettingsUse the View Window to specify the range of the x- and y-ax

19990401kkkkk Displaying the DerivativeDescriptionIn addition to using Trace to display coordinates, you can also display the derivative at thecurrent

19990401Example Read coordinates and derivatives along the graph of the functionshown below.Y1 = x2 – 3Use the following V-Window settings.Xmin = –5,

19990401kkkkk Graph to TableDescriptionYou can use trace to read the coordinates of a graph and store them in a number table. Youcan also use Dual Gra

19990401Example Save, in a table, the coordinates in the vicinity of the points ofintersection at X = 0 for the two graphs shown below, and store thet

19990401kkkkk Coordinate RoundingDescriptionThis function rounds off coordinate values displayed by Trace.Set Up1. Draw the graph.Execution2. Press 2(

19990401Example Use coordinate rounding and display the coordinates in the vicinity ofthe points of intersection for the two graphs produced by thefun

19990401kkkkk Calculating the RootDescriptionThis feature provides a number of different methods for analyzing graphs.Set Up1. Draw the graphs.Executi

19990401Example Draw the graph shown below and calculate the root for Y1.Y1 = x(x + 2)(x – 2)Use the following V-Window settings.Xmin = –6.3, Xmax = 6

19990401kkkkk Calculating the Point of Intersection of Two GraphsDescriptionUse the following procedure to calculate the point of intersection of two

19990401Example Graph the two functions shown below, and determine the point ofintersection between Y1 and Y2.Y1 = x + 1, Y2 = x2Use the following V-

199904015-2-2Controlling What Appears on a Graph Screenu V-Window Setting Precautions•Inputting zero for Tθ ptch causes an error.•Any illegal input (o

19990401k Determining the Coordinates for Given PointsDescriptionThe following procedure describes how to determine the y-coordinate for a given x, an

19990401Example Graph the two functions shown below and then determine the y-coordinate for x = 0.5 and the x-coordinate for y = 2.2 on graph Y2.Y1 =

19990401kkkkk Calculating the lntegral Value for a Given RangeDescriptionUse the following procedure to obtain integration values for a given range.Se

19990401Example Graph the function shown below, and then determine the integral valueat (–2, 0).Y1 = x(x + 2)(x – 2)Use the following V-Window setting

19990401kkkkk Conic Section Graph AnalysisYou can determine approximations of the following analytical results using conic sectiongraphs.•Focus/vertex

19990401u To calculate the focus, vertex and latus rectum[G-SLV]-[Focus]/[Vertex]/[Length]Example To determine the focus, vertex and latus rectum for

19990401u To calculate the center and radius [G-SLV]-[Center]/[Radius]Example To determine the center and radius for the circle(X + 2)2 + (Y + 1)2 = 2

19990401i4(G-SLV)h(Y-Icpt)(Calculates the y-intercept.)•Press e to calculate the second set of x-/y-intercepts. Pressing d returns to the firstset of

19990401u To draw and analyze the asymptotes [G-SLV]-[Asympt]Example To draw the asymptotes for the hyperbola(X – 1)2(Y – 1)2–––––––– – –––––––– = 1