Casio CFX-9850G PLUS 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)
A selection of graph commands also makes it possible to incor-
porate 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

112
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.
• {SEL} ... {draw/non-draw status}
• {DEL} ... {function delete}
• {TYPE} ... {graph type menu}
• {COLR} ... {graph color}
• {GMEM} ... {graph memory save/recall}
• {DRAW} ... {graph draw}
Memory area
Use f and c to change selection.
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113
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 .......... Spacing of y-axis increments
• {INIT}/{TRIG}/{STD} ... View Window {initial settings}/{initial settings using
specified angle unit}/{standardized settings}
• {STO}/{RCL} ... View Window setting {store}/{recall}
The nearby illustration shows the meaning
of each of these parameters.
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
parameters 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
P. 11 5
P. 11 6
X min X scale
Y min
Y max
X max
Y scale
(x, y)

114
The nearby 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 107
or less than 10-2, are automatically converted to a 7-digit mantissa (including
negative sign) plus a 2-digit exponent.
•The only keys that enabled while the View Window is on the display are: a
to 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
allowable 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, causes the axis to be 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 the y-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.
•When View Window values are changed, the graph display is cleared and the
newly set axes only are displayed.
•View Window settings 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.
8 - 2 View Window (V-Window) Settings
(r , θ ) or
( X, Y )
min
max
pitch

115
kk
kk
kInitializing and Standardizing the View Window
uu
uu
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.
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).
uu
uu
uTo standardize the View Window
Press !3 (V-Window) 3(STD) to standardize the View Window to the
following settings.
Xmin = –10 Ymin = –10
Xmax = 10 Ymax = 10
Xscale = 1 Yscale = 1
View Window (V-Window) Settings 8 - 2

116
8 - 2 View Window (V-Window) Settings
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 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.
uu
uu
uTo recall View Window settings
Pressing 5(RCL) 1(V·W1) recalls the contents of View Window memory
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],
[Y min value], [Y max value], [Y scale value],
[T, θ min value], [T, θ max value], [T, θ pitch value]

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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.
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
the graph type menu, which contains the following items.
•{Y=}/{r=}/{Parm}/{X=c} ... {rectangular coordinate}/{polar coordinate}/
{parametric}/{X=constant} graph
•{Y>}/{Y<}/{Ytt
tt
t}/{Yss
ss
s} ... {Y>f(x)}/{Y<f(x)}/{Y>f(x)}/{Y<f(x)} inequality graph
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.)
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= expres-
sions, 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.)

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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.
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.
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.)
8 - 3 Graph Function Operations

119
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.)
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 or 6(NO) to abort the procedure
without 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
uu
uu
uTo specify the graph color
The default color for graph drawing is blue, but you can change the color to
orange or green if you want.
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
whose graph color you want to change.
2. Press 4(COLR) to display a color menu, which contains the following items.
• {Blue}/{Orng}/{Grn} ... {blue}/{orange}/{green}
3. Press the function key for the color you want to use.
Graph Function Operations 8 - 3
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120
uu
uu
uTo specify the draw/non-draw status of a graph
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.)
cc1(SEL)
c1(SEL)
6(DRAW) or w
(Draws the graphs.)
•Pressing !6(G↔T) or Areturns to the Graph Function Menu.
8 - 3 Graph Function Operations
Unhighlights

121
•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)
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.
•Apolar coordinate (r=) or parametric graph will appear coarse if the settings
you make in the View 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.
•Attempting to draw a graph for an expression in which X is input for an X =
constant expression results in an error.
Graph Function Operations 8 - 3
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122
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.
•All graph functions in the currently displayed Graph Function Menu (up to 20)
•Graph types
•Graph colors
•Draw/non-draw status
•View Window settings (1 set)
uu
uu
uTo store graph functions in graph memory
Pressing 5(GMEM) 1(STO) 1(GM1) stores the selected graph function into
graph memory GM1.
•There are six graph memories numbered GM1 to GM6.
•Storing a function in a memory area that already contains a function replaces
the existing function with the new one.
•If the data exceeds the calculator’s remaining memory capacity, an error
occurs.
uu
uu
uTo recall a graph function
Pressing 5(GMEM) 2(RCL) 1(GM1) recalls the contents of graph memory
GM1.
•Recalling data from graph memory causes any data currently on the Graph
Function Menu to be deleted.
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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
• {Y>}/{Y<}/{Ytt
tt
t}/{Yss
ss
s} ... {Y>f(x)}/{Y<f(x)}/{Y>f(x)}/{Y<f(x)} inequality graph
uu
uu
uTo graph using rectangular coordinates (Y =) [Sketch]-[GRPH]-[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 “Y=” for Func Type and then press J.
2. Input the rectangular coordinate (Y =) expression.
!4(Sketch)1(Cls)w
5(GRPH)1(Y =) cvx+dv-e
3. Press wto draw the graph.
•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.

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uu
uu
uTo graph using polar coordinates (r=) [Sketch]-[GRPH]-[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 T, θ min = 0
Xmax = 3 Ymax = 2 T, θ max = π
Xscale = 1 Yscale = 1 T, θ pitch = π÷36
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=).
!4(Sketch)1(Cls)w
5(GRPH)2(r=)csdv
4. Press wto draw the graph.
•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.
8 - 5 Drawing Graphs Manually

125
uu
uu
uTo graph parametric functions [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 = –12 T, θ min = 0
Xmax = 20 Ymax = 12 T, θ max = 4π
Xscale = 5 Yscale = 5 T, θ pitch = π÷36
1. In the set up screen, specify “Parm” for Func Type.
2. Specify “Rad” (radians) as the angle unit and then press 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.
uu
uu
uTo graph X = constant [Sketch]-[GRPH]-[X=c]
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 “X=c” for Func Type and then press J.
Drawing Graphs Manually 8 - 5

126
2. Input the expression.
!4(Sketch)1(Cls)w
5(GRPH)4(X = c)d
3. Press wto draw the graph.
uu
uu
uTo graph inequalities [Sketch]-[GRPH]-[Y>]/[Y<]/[Y≥]/[Y≤]
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 “Y>” for Func Type and then press 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.
8 - 5 Drawing Graphs Manually

127
uu
uu
uTo draw an integration graph [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:
∫
–2
1
(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.
!4(Sketch)1(Cls)w
5(GRPH)5(G∫dx)(v+c)(v-b)
(v-d),-c,b,bE-e
3. Press wto draw the graph.
•Before drawing an integration graph, be sure to always press !4(Sketch)
1(Cls) to clear the screen.
•You can also incorporate an integration graph command into programs.
Drawing Graphs Manually 8 - 5

128
8-6 Other Graphing Functions
The functions described in this section tell you how to read the x- and y-coordi-
nates 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.
kk
kk
kConnect Type and Plot Type Graphs (Draw Type)
You can use the Draw Type setting of the set up screen to specify one of two
graph types.
•Connect
Points are plotted and connected by lines to create a curve.
•Plot
Points are plotted without being connected.
kk
kk
kTrace
With trace, you can move a flashing pointer along a graph with the cursor keys
and obtain readouts of coordinates at each point. The following shows the different
types of coordinate readouts produced by trace.
•Rectangular Coordinate Graph • Polar Coordinate Graph
•Parametric Function Graph • X = Constant Graph
•Inequality Graph
uu
uu
uTo use trace to read coordinates
Example To determine the points of intersection for graphs produced by
the following functions:
Y1 = x2– 3 Y2 = –x+ 2
Use the following View Window parameters.
Xmin = –5 Ymin = –10
Xmax = 5 Ymax = 10
Xscale = 1 Yscale = 2
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129
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 dto move the pointer to the first intersection.
d~d
•Pressing dand emoves the pointer along the graph. Holding down either
key moves the pointer at high speed.
3. Use fand cto move the pointer between the two graphs.
4. Use eto move the pointer to the other intersection.
e~e
•To abort a trace operation, press 1(Trace).
•Do not press the Akey while performing a trace operation.
uu
uu
uTo display the derivative
If the Derivative item in the set up screen is set to “On”, the derivative appears on
the display along with the coordinate values.
x/y coordinate values
Other Graphing Functions 8 - 6
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130
•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.
•Setting the Coord item in the set up screen to “Off” turns display of the
coordinates for the current pointer location off.
uu
uu
uScrolling
When the graph you are tracing runs off the display along either the x- or y-axis,
pressing the eor dcursor key causes the screen to scroll in the correspond-
ing direction eight dots.
•You can scroll only rectangular coordinate and inequality graphs while tracing.
You cannot scroll polar coordinate graphs, parametric function graphs, or X =
constant graphs.
•The graph on the screen does not scroll when you are tracing while the Dual
Screen Mode is set to “Graph” or “G to T”.
•Trace can be used only immediately after a graph is drawn. It cannot be used
after changing the settings of a graph.
•The x- and y-coordinate values at the bottom of the screen are displayed
using a 12-digit mantissa or a 7-digit mantissa with a 2-digit exponent. The
derivative is displayed using a 6-digit mantissa.
•You cannot incorporate trace into a program.
•You can use trace on a graph that was drawn as the result of an output
command (^), which is indicated by the “-Disp-” indicator on the screen.
kk
kk
kScroll
You can scroll a graph along its x- or y-axis. Each time you press f, c, d, or
e, the graph scrolls 12 dots in the corresponding direction.
8 - 6 Other Graphing Functions
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