Casio FX-9750G User manual

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)
Aselection of graph commands also makes it possible to incorpo-
rate graphing into programs.
8-1 Before Trying to Draw a Graph
8-2 View Window (V-Window) Settings
8-3 Graph Function Operations
8-4 Graph Memory
8-5 Drawing Graphs Manually
8-6 Other Graphing Functions
8-7 Picture Memory
8-8 Graph Background
Chapter
8

126
8-1 Before Trying to Draw a Graph
kk
kk
kEntering 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.
1(SEL)........ Draw/non-draw status
2(DEL) ....... Graph delete
3(TYPE) ..... Graph Type Menu
5(GMEM) ... Graph memory save/recall
6(DRAW).... Draws graph
Memory area
Use
f and c to change selection.
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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 spac-
ing between the increments on each axis. You should always set the View Window
parameters you want to use before drawing a graph. Press !3to display the
View Window.
1. Press !3 to display the View Window.
!3(V-Window)
1(INIT)........ View Window initial settings
2(TRIG)...... View Window initial settings using specified angle unit
3(STD) ....... Standardized View Window settings
4(STO) ....... Store View Window settings to View Window memory.
5(RCL) ....... Recall View Window settings from View Window memory.
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 ........... Spacing of y-axis increments
The following illustration shows the meaning of each of these parameters.
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X min X scale
Y min
Y max
X max
Y scale
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128
2. Input a value for a parameter and press w. The calculator automatically selects
the next parameter for input.
• You can also select a parameter using the cand fkeys.
• There are actually nine View Window parameters. The remaining three param-
eters appear on the display when you move the highlighting down past the Y
scale parameter by inputting values and pressing c.
T, θ min .......... T, θ minimum values
T, θ max......... T, θ maximum values
T, θ pitch ........ T, θ pitch
The following illustration shows the meaning of each of these parameters.
3. To exit the View Window, press Jor !Q.
• Pressing wwithout 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. Values greater than 107or
less than 10-2, are automatically converted to a 7-digit mantissa (including nega-
tive sign) plus a 2-digit exponent.
• The only keys that enabled while the View Window is on the display are: ato
j, ., E, -, f, c, d, e, +, -, *, /, (, ), !7,
J, !Q.You can use -or -to input negative values.
• The existing value remains unchanged if you input a value outside the allow-
able range or in the case of illegal input (negative sign only without a value).
• Inputting a View Window range so the min value is greater than the max value,
the axis is inverted.
• You can input expressions (such as 2π) as View Window parameters.
• When the View Window setting does not allow display of the axes, the scale for
they-axis is indicated on either the left or right edge of the display, while that for
the x-axis is indicated on either the top or bottom edge.
8 - 2 View Window (V-Window) Settings
(r , θ ) or
( X, Y )
min
max
pitch

129
• When View Window values are changed, the graph display is cleared and the
newly set axes only are displayed.
• View Window setting may cause irregular scale spacing.
• Setting maximum and minimum values that create too wide of a View Window
range can result in a graph made up of disconnected lines (because portions of
the graph run off the screen), or in graphs that are inaccurate.
• The point of deflection sometimes exceeds the capabilities of the display with
graphs that change drastically as they approach the point of deflection.
• Setting maximum and minimum values that create to narrow of a View Window
range can result in an error (Ma ERROR).
kk
kk
kInitializing and Standardizing the View Window
uu
uu
uTo initialize the View Window
a. 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
b. Press !3(V-Window) 2(TRIG) to initialize the View Window to the follow-
ing settings.
Deg Mode
Xmin = –540 Ymin = –1.6
Xmax = 540 Ymax = 1.6
Xscale = 90 Yscale = 0.5
Rad Mode
Xmin = –9.4247779
Xmax = 9.42477796
Xscale = 1.57079632
Gra Mode
Xmin = –600
Xmax = 600
Xscale = 100
• The settings for Y min, Y max, Y pitch, T/
θ min, T/ θ max, and T/ θ pitch remain
unchanged when you press 2(TRIG).
View Window (V-Window) Settings 8 - 2

130
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8 - 2 View Window (V-Window) Settings
uu
uu
uTo standardize the View Window
Press !3 (V-Window) 3(STD) to standardize the View Window to the follow-
ing settings.
Xmin = –10 Ymin = –10
Xmax = 10 Ymax = 10
Xscale = 1 Yscale = 1
kk
kk
kView Window Memory
You can store up to six sets of View Window settings in View Window memory for
recall when you need them.
uu
uu
uTo save View Window settings
Example To save the following View Window settings :
Xmin = –5 Ymin = –5
Xmax = 5 Ymax = 5
Xscale = 1 Yscale = 1
4(STO)
1(V·W1)
• Storing View Window settings in a memory area (V·W1 through V·W6) that al-
ready contains settings replaces the existing settings with the new ones.
uu
uu
uTo recall View Window settings
Example To recall the View Window settings in V·W1
5(RCL)
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1(V·W1)
• Recalling View Window settings causes the settings currently on the display to be
deleted.
• You can change View Window settings in a program using the following syntax.
View Window [X min value], [X max value], [X scale value],
[Ymin value], [Y max value], [Y scale value],
[T,
θ min value], [T, θ max value], [T, θ pitch value]
View Window (V-Window) Settings 8 - 2

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8-3 Graph Function Operations
You can store up to 20 functions in memory. Functions in memory can be edited,
recalled, and graphed. The types of functions that can be stored in memory are:
rectangular coordinate functions, polar coordinate functions, parametric functions,
inequalities, and X = constant expressions.
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 Menu is on the display, press 3(TYPE) to display a
GraphType Menu.
3(TYPE)
1(Y =) ......... Rectangular coordinate
graph
2(r=).......... Polar coordinate graph
3(Parm)...... Parametric graph
4(X = c) ...... X = constant graph
6(g) ........... Next menu
6(g)
1(Y >) ......... Y > f (x) inequality
2(Y <) ......... Y < f (x) inequality
3(Y ≥) ......... Y >f (x) inequality
4(Y ≤) ......... Y <f
(x) inequality
6(g) ........... Previous menu
2. Press the function key that corresponds to the graph type you want to specify.
kk
kk
kStoring Graph Functions
uu
uu
uTo store a rectangular coordinate function (Y =)
Example To store the following expression in memory area Y1 :
y= 2 x2– 5
3(TYPE)1(Y =)
(Specifies rectangular coordinate
expression.)
cvx-f
(Inputs expression.)
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w
(Stores expression.)
• You will not be able to store the expression in an area that already contains a
parametric function. Select another area to store your expression or delete the
existing parametric function first. This also applies when storing r= expressions,
X = constant expressions, and ineqalities.
uu
uu
uTo store a polar coordinate function (r=)
Example To store the following expression in memory area r2 :
r= 5 sin 3 θ
3(TYPE)2(r=)
(Specifies polar coordinate expression.)
fsdv
(Inputs expression.)
w
(Stores expression.)
uu
uu
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 xexpression.)
dcvw
(Inputs and stores yexpression.)
• 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. Select another area to store your expression or delete
the existing expression first.
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134
8 - 3 Graph Function Operations
uu
uu
uTo store an X = constant expression
Example To store the following expression in memory area X4 :
X = 3
3(TYPE)4(X = c)
(Specifies X = constant expression.)
d
(Inputs expression.)
w
(Stores expression.)
• Inputting X, Y, T, r, or θ for the constant in the above procedures causes an error
(Syn ERROR).
uu
uu
uTo store an inequality
Example To store the following inequality in memory area Y5 :
y> x2– 2x– 6
3(TYPE)6(g)1(Y>)
(Specifies an inequality.)
vx-cv-g
(Inputs expression.)
w
(Stores expression.)
kk
kk
kEditing Functions in Memory
uu
uu
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.)

135
uu
uu
uTo delete a function
1. While the Graph Function Menu is on the display, press for cto display the
cursor and move the highlighting to the area that contains the function you want
to delete.
2. Press 2(DEL).
3. Press 1(YES) to delete the function for 6(NO) to abort the procedure with-
out deleting anything.
Parametric functions come in pairs (Xt and Yt).
When editing a parametric function, clear the graph functions and re-input from the
beginning.
kk
kk
kDrawing a Graph
Before actually drawing a graph, you should first make the following specification.
uu
uu
uTo specify the draw/non-draw status of a graph
You can specify which functions out of those stored in memory should be used for a
draw operation.
• Graphs for which there is no draw/non-draw status specification are not drawn.
Example To select the following functions for drawing :
Y1 = 2x2– 5
r2 = 5 sin3 θ
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.)
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Graph Function Operations 8 - 3
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cc1(SEL)
c1(SEL)
6(DRAW) or w
(Draws graphs.)
• Pressing !6(G↔T) or Areturns to the Graph Function Menu.
• You can use the set up screen settings to alter the appearance of the graph
screen as shown below.
• Grid: On
This setting causes dots to appear at the grid intersects on the display.
• Axes: Off
This setting clears the axis lines from the display.
• Label: On
This setting displays labels for the x- and y-axes.
8 - 3 Graph Function Operations
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• A polar coordinate (r=) or parametric graph will appear coarse if the settings
you make in the View Window cause theT, 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 be-
tween the T, θ min and T, θ max settings, on the other hand, the graph will take
a very long time to draw.
• Attempting to draw a graph for an expression in which X is input for an X =
constant expression results in an error (Syn ERROR).
Graph Function Operations 8 - 3

138
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 stored in graph memory.
• All graph functions in the currently displayed Graph Function Menu (up to 20)
• Graph types
• Draw/non-draw status
• View Window settings (1 set)
uu
uu
uTo save graph functions in graph memory
Example To store the graph functions shown on the screen below in graph
memory GM1
5(GMEM)
1(STO)
1(GM1)
• Storing data in a memory area (GM1 through GM6) that already contains data
replaces the existing data with the new data.
• If the data exceeds the calculator’s remaining memory capacity, an error (Mem
ERROR) occurs.
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uu
uu
uTo recall graph functions from graph memory
Example To recall the data in graph memory GM1
5(GMEM)
2(RCL)
1(GM1)
• Recalling data from graph memory causes any data currently on the Graph Func-
tion Menu to be deleted.
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140
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.
!4(Sketch)
5(GRPH)
1(Y =) ......... Rectangular coordinate graph
2(r=).......... Polar coordinate graph
3(Parm)...... Parametric graph
4(X = c) ...... X = constant graph
5(G∫dx) ....... For drawing integration graphs
6(g) ........... Next menu
6(g)
1(Y >) ......... Y > f (x) inequality
2(Y <) ......... Y < f (x) inequality
3(Y ≥) ......... Y >f
(x) inequality
4(Y ≤) ......... Y <f (x) inequality
6(g) ........... Previous menu
uu
uu
uTo graph using rectangular coordinates (Y =)
You can graph functions that can be expressed in the format y= f(x).
Example To graph y= 2x2+ 3x– 4
Use the following View Window parameters.
Xmin = –5 Ymin = –10
Xmax = 5 Ymax = 10
Xscale = 2 Yscale = 5
1. In the set-up screen, specify the appropriate graph type for Func Type.
!Zc1(Y =)J
2. Input the rectangular coordinate (Y =) expression.
!4(Sketch)1(Cls)w
5(GRPH)1(Y =)
cvx+dv-e
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3. Press wto draw the graph.
w
• You can draw graphs of the following built-in scientific functions.
• sin x• cos x• tan x
• sin–1 x• cos–1 x• tan–1 x
• sinh x• cosh x• tanh x
• sinh–1 x• cosh–1 x• tanh–1 x
• • x2• log x
• lnx• 10x• ex
• x–1 • 3
View Window settings are made automatically for built-in graphs.
uu
uu
uTo graph using polar coordinates (r=)
You can graph functions that can be expressed in the format r= f ( θ ).
Example To graph r= 2 sin3 θ
Use the following View Window parameters.
Xmin = –3 Ymin = –2
Xmax = 3 Ymax = 2
Xscale = 1 Yscale = 1
T,
θ min = 0 T, θ max = π
T, θ pitch = π÷36
1. In the set-up screen, specify the appropriate graph type for Func Type.
!Zc2(r=)
2. Set the default unit of angular measurement to radians (Rad).
ccc2(Rad)J
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142
3. Input the polar coordinate expression (r=).
!4(Sketch)1(Cls)w
5(GRPH)2(r=)
csdv
4. Press wto draw the graph.
w
• You can draw graphs of the following built-in scientific functions.
• sin θ • cos θ • tan θ
• sin–1 θ • cos–1 θ • tan–1 θ
• sinh θ • cosh θ • tanh θ
• sinh–1 θ • cosh–1 θ • tanh–1 θ
• θ • θ
2• log
θ
• ln θ • 10
θ
• e
θ
• θ
–1 • 3
θ
• View Window settings are made automatically for built-in graphs.
uu
uu
uTo graph parametric functions
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 = –12
Xmax = 20 Ymax = 12
Xscale = 5 Yscale = 5
T,
θ min = 0 T, θ max = 4π
T,
θ pitch = π÷36
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143
1. In the set-up screen, specify the appropriate graph type for Func Type.
!Zc3(Parm)
2. Set the default angle unit to radians (Rad).
ccc2(Rad)J
3. Input the parametric functions.
!4(Sketch)1(Cls)w
5(GRPH)3(Parm)
hcv-ccd.fv,
hsv-csd.fv)
4. Press wto draw the graph.
w
uu
uu
uTo graph X = constant
You can graph functions that can be expressed in the format X = constant.
Example To graph X = 3
Use the following View Window parameters.
Xmin = –5 Ymin = –5
Xmax = 5 Ymax = 5
Xscale = 1 Yscale = 1
1. In the set-up screen, specify the appropriate graph type for Func Type.
!Zc4(X = c)J
2. Input the expression.
!4(Sketch)1(Cls)w
5(GRPH)4(X = c)d
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144
3. Press wto draw the graph.
w
uu
uu
uTo graph inequalities
You can graph inequalities that can be expressed in the following four formats.
• y> f (x)
• y< f (x)
• y>f
(x)
• y<f (x)
Example 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. In the set-up screen, specify the appropriate graph type for Func Type.
!Zc6(g)1(Y>)J
2. Input the inequality.
!4(Sketch)1(Cls)w
5(GRPH)6(g)
1(Y>)vx-cv-g
3. Press wto draw the graph.
w
8 - 5 Drawing Graphs Manually