Casio ALGEBRA FX 2.0 Plus User manual

19990401
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
5
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5-1-1
Sample Graphs
5-1 Sample Graphs
kk
kk
kHow 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.
Execution
2. Input the function you want to graph.
Here you would use the V-Window to specify the range and other parameters of the
graph. See 5-2-1.
3. Draw the graph.

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5-1-2
Sample Graphs
○○○○○
Example To graph y= 3x2
Procedure
1mGRPH •TBL
2dvxw
35(DRAW) (or w)
Result Screen

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5-1-3
Sample Graphs
kk
kk
kHow 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.
Execution
2. Specify the function type and input the function whose graph you want to draw.
You can use the GRPH •TBL Mode to draw a graph for the following types of expres-
sions: rectangular coordinate expression, polar coordinate expression, parametric
function, X = constant expression, inequality.
3(TYPE) b(Y =) ... rectangular coordinates
c(r=) ... polar coordinates
d(Param) ... parametric function
e(X = c) ... X = constant function
f(INEQUA)b(Y>)~e(Y<) ... inequality
g(CONV)b('Y=)~f('Y<) ... changes the function type
Repeat this step as many times as required to input all of the functions you want.
Next you should specify which of the functions among those that are stored in memory
you want to graph (see 5-3-6). If you do not select specific functions here, the graph
operation will draw graphs of all the functions currently stored in memory.
3. Draw the graph.
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5-1-4
Sample Graphs
○○○○○
Example Input the functions shown below and draw their graphs
Y1 = 2x2– 3, r2 = 3sin2 θ
Procedure
1mGRPH •TBL
23(TYPE)b(Y=)cvx-dw
3(TYPE)c(r=)dscvw
35(DRAW)
Result Screen
(Param) (INEQUA) (Plot)

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5-1-5
Sample Graphs
kk
kk
kHow 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. Use the cursor fc keys to specify one of the function type as follows.
3. Input values for the required variables.
4. Graph the function.
Graph Type Function
Parabola X = A (Y – K)2+ H
X = AY2+ BY + C
Y = A (X – H)2+ K
Y = AX2+ BX + C
Circle (X – H)2+ (Y – K)2= R2
AX2+ AY2+ BX + CY + D = 0
Ellipse (X – H)2(Y – K)2
–––––––– + –––––––– = 1
A2B2
Hyperbola (X – H)2(Y – K)2
–––––––– – –––––––– = 1
A2B2
(Y – K)2(X – H)2
–––––––– – –––––––– = 1
A2B2

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5-1-6
Sample Graphs
○○○○○
Example Graph the circle (X–1)2+ (Y–1)2= 22
Procedure
1mCONICS
2ccccw
3bwbwcw
46(DRAW)
Result Screen
(Parabola) (Ellipse) (Hyperbola)

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5-2 Controlling What Appears on a Graph Screen
kk
kk
kV-Window (View 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 V-Window parameters you
want to use before graphing.
uTo make V-Window settings
1. From the Main Menu, enter the GRPH •TBL Mode.
2. Press !K(V-Window) to display the V-Window setting screen.
Rectangular coordinate parameter
Xmin … Minimum x-axis value
Xmax … Maximum x-axis value
Xscale … Spacing of x-axis increments
Xdot … Value that corresponds to one x-axis dot
Ymin … Minimum y-axis value
Ymax … Maximum y-axis value
Yscale … Spacing of y-axis increments
Polar coordinate parameter
T θ min ... T, θ minimum values
T θ max ... T, θ maximum values
T θ ptch ... T, θ pitch
3. Press cto move the highlighting and input an appropriate value for each parameter,
pressing wafter each.
• {INIT}/{TRIG}/{STD}… V-Window {initial settings}/{initial settings using specified
angle unit}/{standardized settings}
•{STO}/{RCL} … V-Window setting {store}/{recall}
After settings are the way you want them, press ior !i(QUIT) to exit the V-Window
setting screen.*1
5-2-1
Controlling What Appears on a Graph Screen
*1Pressing wwithout inputting anything while k
is displayed exits the View Window setting
screen.
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5-2-2
Controlling What Appears on a Graph Screen
uV-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 min, T θ ptch becomes negative.
•You can input expressions (such as 2π) as V-Window parameters.
•When the V-Window setting produces an axis that does not fit on the display, the scale
of the axis is indicated on the edge of the display closest to the origin.
•Changing the V-Window settings clears the graph currently on the display and
replaces it with the new axes only.
•Changing the Xmin or Xmax value causes the Xdot value to be adjusted automatically.
Changing the Xdot value causes the Xmax value to be adjusted automatically.
•Apolar coordinate (r=) or parametric graph will appear coarse if the settings you
make in the V-Window cause the T, θ pitch value to be too large, relative to the
differential between the T, θ min and T, θ max settings. If the settings you make cause
the T, θ pitch value to be too small relative to the differential between the T, θ min and
T, θ max settings, on the other hand, the graph will take a very long time to draw.
•The following is the input range for V-Window parameters.
–9.999999999E97 to 9.999999999E97

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kk
kk
kInitializing and Standardizing the V-Window
uTo 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. Press 1(INIT) to initialize the V-Window.
Xmin = –6.3, Xmax = 6.3, Xscale = 1 Xdot = 0.1
Ymin = –3.1, Ymax = 3.1, Yscale = 1
T θ min = 0, T θ max = 2π (rad), T θ ptch = 2π /60 (rad)
uTo initialize the V-Window in accordance with an angle unit
In step 3 of the procedure under “To initialize the V-Window” above, press 2(TRIG) to
initialize the V-Window in accordance with an angle unit.
Xmin = –3π(rad), Xmax = 3π (rad), Xscale = π /2 (rad), Xdot = π /21 (rad),
Ymin = –1.6, Ymax = 1.6, Yscale = 0.5
uTo standardize the V-Window
The following are the standard V-Window settings of this calculator.
Xmin = –10, Xmax = 10, Xscale = 1, Xdot = 0.15873015,
Ymin = –10, Ymax = 10, Yscale = 1,
T θ min = 0, T θ max = 2π (rad), T θ ptch = 2π /60 (rad)
In step 3 of the procedure under “To initialize the V-Window” above, press 3(STD) to
standardize V-Window settings in accordance with the above.
5-2-3
Controlling What Appears on a Graph Screen
#Initialization and standardization cause T θ
min, T θ max, T θ ptch values to change
automatically in accordance with the current
angle unit setting as shown below.
Deg Mode:
T θ min = 0, T θ max = 360, T θ ptch = 6
Gra Mode:
T θ min = 0, T θ max = 400, T θ ptch = 400/60
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kk
kk
kV-Window Memory
You can store up to six sets of V-Window settings in V-Window memory for recall when you
need them.
uTo store V-Window settings
1. From the Main Menu, enter the GRPH •TBL Mode.
2. Press !K(V-Window) to display the V-Window setting screen, and input the values
you want.
3. Press 4(STO) to display the pop-up window.
4. Press a number key to specify the V-Window memory where you want to save the
settings, and then press w. Pressing bwstores the settings in V-Window Memory
1 (V-Win1).
uTo recall V-Window memory settings
1. From the Main Menu, enter the GRPH •TBL Mode.
2. Press !K(V-Window) to display the V-Window setting screen.
3. Press 5(RCL) to display the pop-up window.
4. Press a number key to specify the V-Window memory number for the settings you want
to recall, and then press w. Pressing bwrecalls the settings in V-Window Memory
1 (V-Win1).
5-2-4
Controlling What Appears on a Graph Screen
#Storing V-Window settings to a memory that
already contains setting data replaces the
previous data with the new settings.
#Recalling settings causes the current V-Window
settings to be replaced with those recalled from
memory.

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kk
kk
kSpecifying 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.
2. Make V-Window settings.
Execution
3. Specify the function type and input the function. The following is the syntax for function
input.
Function ,!+( [ )Start Point ,End Point !-( ] )
4. Draw the graph.
5-2-5
Controlling What Appears on a Graph Screen

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5-2-6
Controlling What Appears on a Graph Screen
○○○○○
Example Graph y= x2+ 3x– 2 within the range – 2 <x <4
Use the following V-Window settings.
Xmin = –3, Xmax = 5, Xscale = 1
Ymin = –10, Ymax = 30, Yscale = 5
Procedure
1m GRPH •TBL
2!K(V-Window) -dwfwbwc
-bawdawfwi
33(TYPE)b(Y=)vx+dv-c,
!+( [ )-c,e!-( ] )w
45(DRAW)
Result Screen
#You can specify a range when graphing
rectangular expressions, polar expressions,
parametric functions, and inequalities.

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5-2-7
Controlling What Appears on a Graph Screen
kk
kk
kZoom
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.
c(Factor)
d(In)/e(Out) ... Factor zoom
The graph is enlarged or reduced in accordance with the factor
you specify, centered on the current pointer location.
f(Auto) ...Auto zoom
V-Window y-axis settings are automatically adjusted so the
graph fills the screen along the y-axis.
g(Orig) ...Original size
Returns the graph to its original size following a zoom opera-
tion.
h(Square) ... Graph correction
V-Window x-axis values are corrected so they are identical to
the y-axis values.
i(Rnd) ... Coordinate rounding
Rounds the coordinate values at the current pointer location.
j(Intg) ... Integer
Each dot is given a width of 1, which makes coordinate values
integers.
v(Pre) ...Previous
V-Window parameters are returned to what they were prior to
the last zoom operation.
l(QUICK) ... Quick zoom
Redraws the graph in accordance with the settings stored in a
selected V-Window memory.
Box zoom range specification
3. Use the cursor keys to move the pointer ( ) in the center of the screen to the location
where you want one corner of the box to be, and then press w.
4. Use the cursor keys to move the pointer. This causes a box to appear on the screen.
Move the cursor until the area you want to enlarge is enclosed in the box, and then
press wto enlarge it.

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5-2-8
Controlling What Appears on a Graph Screen
#You must specify two different points for box
zoom, and the two points cannot be on a straight
line vertically or horizontally from each other.
○○○○○
Example Graph y= (x+ 5)(x+ 4)(x+ 3), and then perform a box zoom.
Use the following V-Window settings.
Xmin = –8, Xmax = 8, Xscale = 2
Ymin = – 4, Ymax = 2, Yscale = 1
Procedure
1m GRPH •TBL
!K(V-Window) -iwiwcwc
-ewcwbwi
3(TYPE)b(Y=)(v+f)(v+e)
(v+d)w
5(DRAW)
22(ZOOM)b(Box)
3d~dw
4d~d,f~fw
Result Screen

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5-2-9
Controlling What Appears on a Graph Screen
kk
kk
kFactor 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 x-axis and
y-axis zoom factor. Input the values you want and then press i.
3. Press 2(ZOOM)d(In) to enlarge the graph, or 2(ZOOM)e(Out) to reduce it. The
graph is enlarged or reduced centered on the current pointer location.
4. Use the cursor keys to move the cursor to the point upon which you want the zoom
operation to be centered, and then press wto zoom.

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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 x-and y-axis to see if they are tangent.
Y1 = (x+ 4)(x+ 1)( x– 3), Y2 = 3x+ 22
Use the following V-Window settings.
Xmin = –8, Xmax = 8, Xscale = 1
Ymin = –30, Ymax = 30, Yscale = 5
Procedure
1m GRPH •TBL
!K(V-Window) -iwiwbwc
-dawdawfwi
3(TYPE)b(Y=)(v+e)(v+b)
(v-d)w
dv+ccw
5(DRAW)
22(ZOOM)c(Factor)fwfwi
32(ZOOM)d(In)
4f~f,d~dw
Result Screen
#You can repeat factor zoom to enlarge or
reduce a graph even further.

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kk
kk
kTurning Function Menu Display On and Off
Press uato 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. When you are using the trace function or other functions during which the function menu is
normally not displayed, you can turn on the menu display to execute a menu command.
5-2-11
Controlling What Appears on a Graph Screen
#If a pull-up menu is open when you press u
ato turn off menu display, the pull-up menu
remains on the screen.
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kk
kk
kAbout 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.
Press ito close the Calc Window.
5-2-12
Controlling What Appears on a Graph Screen
#After using the Calc Window to change the
value of a variable connected with a graph or
table, be sure to always execute Re-G (re-
graph) or Re-T (re-calculate table). Doing so
ensures that the displayed graph or table is
current.
#Calc Window cannot be used in the RUN •
MAT Mode while a program is running, or in
combination with Dynamic Graph.
#Calc Window cannot be used in combination
with V-Window or the table range setting screen.
#Complex number calculations cannot be
performed on the Calc Window.
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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.
kk
kk
kSpecifying the Graph Type
Before you can store a graph function in memory, you must first specify its graph type.
1. While the Graph function list is on the display, press 6(g)3(TYPE) to display the
graph type menu, which contains the following items.
•{Y=}/{r=}/{Param}/{X=c} ... {rectangular coordinate}/{polar coordinate}/{parametric}/
{X=constant}*1graph
•{INEQUA}
•{Y>}/{Y<}/{Ytt
tt
t}/{Yss
ss
s} ... {Y>f(x)}/{Y<f(x)}/{Y>f(x)}/{Y<f(x)} inequality graph
•{CONV}
•{'Y=}/{'Y>}/{'Y<}/{'Ytt
tt
t}/{'Yss
ss
s} ... changes the function type
2. Press the number key that corresponds to the graph type you want to specify.
kk
kk
kStoring Graph Functions
uTo store a rectangular coordinate function (Y =) *2
○○○○○
Example To store the following expression in memory area Y1 : y= 2x2– 5
3(TYPE)b(Y =) (Specifies rectangular coordinate expression.)
cvx-f(Inputs expression.)
w(Stores expression.)
uTo store a polar coordinate function (r=) *2
○○○○○
Example To store the following expression in memory area r2 : r= 5 sin3 θ
3(TYPE)c(r=) (Specifies polar coordinate expression.)
fsdv(Inputs expression.)
w(Stores expression.)
*1Attempting to draw a graph for an expression
in which X is input for an X = constant
expression results in an error.
*2A function cannot be stored into a memory area that
already contains a function of a different type from
the one you are trying to store. Select a memory
area that contains a function that is the same type
as the one you are storing, or delete the function in
the memory area to which you are trying to store.
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