Casio CFX-9850G PLUS User manual

Dynamic Graph
The Dynamic Graph Mode of this calculator shows you real-time
representations of changes in a graph as coefficients and terms
are changed. It lets you see what happens to a graph when such
changes are made. For example, you can see the graph change
as illustrated here as the value of coefficient A changes in the
formula y= Ax2.
13-1 Before Using Dynamic Graph
13-2 Storing, Editing, and Selecting Dynamic Graph
Functions
13-3 Drawing a Dynamic Graph
13-4 Using Dynamic Graph Memory
13-5 Dynamic Graph Application Examples
Chapter
13

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13-1 Before Using Dynamic Graph
In the Main Menu, select the DYNA icon and enter the DYNA Mode. When you do
the dynamic function list appears on the screen.
Selected memory area
Press c and f to move.
• {SEL} ... {dynamic Graph draw/non-draw status}
• {DEL} ... {function delete}
• {TYPE} ... {function type specification}
• {VAR} ... {coefficient menu}
• {B·IN} ... {menu of built-in functions*}
• {RCL} ... {recall and execution of Dynamic Graph conditions and screen data}
*The built-in function menu contains the following seven functions.
•Y=AX+B
•Y=A(X+B)2+C
•Y=AX2+BX+C
•Y=AX^3+BX2+CX+D
•Y=Asin(BX+C)
•Y=Acos(BX+C)
•Y=Atan(BX+C)
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13-2 Storing, Editing, and Selecting Dynamic
Graph Functions
In addition to the seven built-in functions, you can input 20 of your own Dynamic
Functions. Once a function is stored in memory, it can be edited and selected
when needed for graphing.
All of the procedures you need to use for storing, editing, and selecting Dynamic
Graph functions are identical to those you use in the GRAPH Mode. For details,
see “8-3 Graph Function Operations”.
•Dynamic Graphs can be one of the following three types only: rectangular
coordinate (Y=), polar coordinate (r=), and parametric.
•You cannot use Dynamic Graph with X=constant or inequality graphs of
functions stored in the GRAPH or TABLE Mode.
•If you try to use Dynamic Graph with a function that does not contain a
variable, a “No Variable” error occurs. If this happens, press Ato clear the
error.
•Dynamic Graph always uses blue to draw graphs. This cannot be changed.
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13-3 Drawing a Dynamic Graph
The following is the general procedure you should use to draw a Dynamic Graph.
1. Select or input a function.
2. Define the dynamic coefficient.
•This is a coefficient whose value changes in order to produce the different
graphs.
•If the dynamic coefficient is already defined from a previous operation, you can
skip this step.
3. Assign values to each of the coefficients of the function.
4. Specify the range of the dynamic coefficient.
•If the range of the dynamic coefficient is already defined from a previous
operation, you can skip this step.
5. Specify the speed of the draw operation.
•If the speed is already defined from a previous operation, you can skip this
step.
6. Draw the Dynamic Graph.
uu
uu
uTo set Dynamic Graph conditions
Example To use Dynamic Graph to graph y= A (x–1)2–1 as the value of
A changes from 2 to 5 in increments of 1
Use the following View Window parameters.
Xmin = – 6.3 Ymin = – 3.1
Xmax = 6.3 Ymax = 3.1
Xscale = 1 Yscale = 1
1. Input the function you want to graph. Here we will edit a built-in function to
input our function.
5(B·IN)
c1(SEL)
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185
2. Display the coefficient menu.
4(VAR) or w
Function being graphed
Coefficient whose value will change
Coefficients in function
• {SEL} ... {selects dynamic coefficient}
• {RANG} ... {dynamic coefficient range settings}
• {SPEED} ... {dynamic Graph drawing speed}
• {AUTO} ... {automatic setting of end and pitch values to match coefficient
values}
• {DYNA} ... {dynamic Graph draw operation}
•The calculator automatically makes the first variable it finds the dynamic
coefficient. To select a different coefficient, use cand fto move the
highlighting to the coefficient you want to use, and the press 1(SEL).
•The letters representing each coefficient are variables, and so the values that
appears on the screen are those currently assigned to each variable. If a
complex number is assigned to a variable, only the integer part appears.
•All variables contained in the currently selected function appear on the display
in alphabetical order.
•If there is more than one function that can be drawn using Dynamic Graph, the
message “Too Many Functions” appears on the display.
•If the value of the dynamic variable is zero and you press 5(AUTO), the
dynamic variable automatically changes to 1 and Dynamic Graphing is
performed.
3. Specify the value of each coefficient.
cw-bw-bw
•If there is more than one coefficient, use fand cto move the highlighting
to each coefficient and input its value.
•Values you input for coefficients are also assigned to the corresponding
variable.
4. Recall the coefficient range menu.
2(RANG)
•The range you set remains in effect until you change it.
Drawing a Dynamic Graph 13 - 3
Dynamic coefficient
Start value
End value
Increment

186
5. Change the range settings.
cwJ
•If you want to change the Dynamic Graph
speed, press 3(SPEED).
You can set the Dynamic Graph speed to any one of the following settings.
Stop & Go: Each step of the Dynamic Graph draw operation is performed
each time you press w.
Slow: 1/2 Normal
Normal: Default speed
Fast: Double Normal
1. Use fand cto move the highlighting to the speed you want to use.
2. Press 1(SEL) to set the highlighted speed.
uu
uu
uTo start the Dynamic Graph draw operation
There are four different variations for Dynamic Graphing.
kk
kk
k10-time Continuous Drawing
Select “Stop” as the draw type (Dynamic Type) to perform 10-time continuous
drawing. With this drawing style, 10 versions of the graph are drawn and then the
draw operation stops automatically.
Example To use 10-time continuous drawing to draw the same graph
that you drew in the previous example (page 184)
1. Display the coefficient menu. Next, display the set up screen and specify
“Stop” for Dynamic Type and then press J.
2. Start drawing of the Dynamic Graph.
6(DYNA)
↓
13 - 3 Drawing a Dynamic Graph
123456
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187
→
←
↓↑
→
←
The above sequence continues to repeat from 1through 4.
Graph is drawn 10 times.
•While the message “One Moment Please!” is shown on the display, you can
press Ato interrupt drawing of the graph and return to the coefficient range
setting display.
•Pressing Awhile the Dynamic Graph is being drawn changes to the drawing
speed setting display. The draw operation is suspended at this time, and you
can view the graph by pressing !6 (G ↔T).
•If you do not want the function and coefficient values shown on the display with
the graph, use the graph function set up display to switch Graph Func “Off”.
•Pressing 5(AUTO) draws up to 11 versions of the Dynamic Graph, starting
from the start (Start) value of the dynamic coefficient.
kk
kk
kContinuous Drawing
When the Dynamic Graph draw type (Dynamic Type) is set to “Cont” (continuous),
drawing of the Dynamic Graph continues until you press A.
Example To continuously draw the same graph that you input in the
previous example (page 184)
1. Display the coefficient menu. Next, display the set up screen and specify
“Cont” for Dynamic Type and then press J.
2. Start drawing of the Dynamic Graph.
6(DYNA)
···→
←···
Drawing a Dynamic Graph 13 - 3
1
4
2
3
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188
•Pressing Awhile the Dynamic Graph is being drawn changes to the drawing
speed setting display. The draw operation is suspended at this time, and you
can view the graph by pressing !6 (G ↔T).
•Selecting “Cont” and then executing a Dynamic Graph operation causes the
graphing operation to repeat until you press A. Be sure that you do not forget
to stop the Dynamic Graph operation after you are finished. Allowing it to
continue will run down the batteries.
kk
kk
kStop & Go Drawing
By selecting “STOP & GO ” as the graph drawing speed, you can draw graphs
one by one. A graph is drawn each time you press w.
Example To use Stop & Go to draw the same graph that you drew in the
previous example (page 184)
1. Display the coefficient value specification display and press 3(SPEED).
2. Use fand cto select “STOP & GO ()” and press 1(SEL) J.
3. Start drawing of the Dynamic Graph.
6(DYNA)
w
···→
←···
w
•Pressing Awhile the Dynamic Graph is being drawn changes to the drawing
speed setting display. The draw operation is suspended at this time, and you
can view the graph by pressing !6 (G ↔T).
kk
kk
kOverwriting
By turning “On” the locus (Locus) setting of the Dynamic Graph, graphs are
sequentially drawn on the same display. The newest graph drawn is easily
identifiable because its color is different from graphs that were previously on the
display.
Example To switch the locus setting on and draw the same graph that
you drew in the previous example (page 184)
1. Display the coefficient menu. Next, display the set up screen and specify “On”
for Locus and then press J.
13 - 3 Drawing a Dynamic Graph
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Drawing a Dynamic Graph 13 - 3
2. Start drawing of the Dynamic Graph.
6(DYNA)
w
···→
←···
w
•Pressing Awhile the Dynamic Graph is being drawn changes to the drawing
speed setting display. The draw operation is suspended at this time, and you
can view the graph by pressing !6 (G↔T).
•Depending on the complexity of the graphs being drawn, it may take some
time for them to appear on the display.
•Trace and zoom features cannot be used on a Dynamic Graph screen.
uu
uu
uTo adjust 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 Ato
change to the speed adjustment menu.
•{
tgtg
tgtg
tg} ... {Each step of the Dynamic Graph draw operation is performed each
time you press w.}
•{>}/{gg
gg
g}/{hh
hh
h} ... {slow (1/2 speed)}/{normal (default speed)}/{fast (double speed)}
• {STO} ... {stores graph conditions and screen data in Dynamic Graph memory}
• {DEL} ... {deletes Dynamic Graph screen data}
2. Press the function key (1to 4) that corresponds to the speed you want to
change to.
•To clear the speed adjustment menu without changing anything, press w.
•Press !6(G↔T) to return to the graph screen.
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13-4 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. Note
that you can store one set of data in memory at any one time.
The following is all of the data that makes up a set.
•Graph functions (up to 20)
•Dynamic Graph conditions
•Set up screen settings
•View Window contents
•Dynamic Graph screen
uu
uu
uTo save data in Dynamic Graph memory
1. While a Dynamic Graph draw operation is being performed, press Ato
change to the speed adjustment menu.
2. Press 5(STO) to store the data.
•If there is already data stored in Dynamic Graph memory, the above operation
replaces it with the new data.
uu
uu
uTo recall data from Dynamic Graph memory
1. Display the Dynamic Graph function list.
2. Press 6(RCL) to recall all the data stored in Dynamic Graph memory.
•Data recalled from Dynamic Graph memory replaces the calculator’s current
graph functions, draw conditions, and screen data. The previous data is lost
when it is replaced.
uu
uu
uTo delete Dynamic Graph screen data
1. Press A6 (DEL).
2. Press 1(YES) to delete the Dynamic Graph screen data, or 6(NO) to
abort the operation without deleting anything.
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Drawing a Dynamic Graph 13 - 3
13-5 Dynamic Graph Application Examples
Example To use Dynamic Graph to graph the parabolas produced by
balls thrown in the air at an initial velocity of 20m/second, at
angles of 30, 45, and 60 degrees. (Angle: Deg)
Use the following View Window parameters.
Xmin = –1 Ymin = –1 T θ min = 0
Xmax = 42 Ymax = 16 T θ max = 6
Xscale = 5 Yscale = 2 pitch = 0.1
With the initial velocity defined as V and the angle defined as θ , the parabolas can
be obtained using the following expressions.
X = Vcos θ T
Y = Vsin θ T – (1/2)gT2
g = 9.8 meters per second
1. Input the functions, making sure to specify
them a “Param” (parametric) type.
2. Display the coefficient menu and specify the dynamic coefficient.
4(VAR)daw
3. Display the coefficient range menu and specify the range values.
2(RANG)
dawgawbfw
4. Start the Dynamic Graph draw operation.
J6(DYNA)
···→
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192