Casio CFX-9970G User manual
Graph Solve
You can use any of the following methods to analyze function
graphs and approximate results.
•Root extraction
•Determination of the maximum and minimum
•Determination of the y-intercept
•Determination of the intersection of two graphs
•Determination of the coordinates at any point (yfor a given x/x
for a given y)
•Determination of the integral for any range
9-1 Before Using Graph Solve
9-2 Analyzing a Function Graph
Chapter
9
144
9-1 Before Using Graph Solve
After using the GRAPH Mode to draw the graph, press !5(G-Solv) to
display a function menu that contains the following items.
•{ROOT}/{MAX}/{MIN}/{Y-ICPT}/{ISCT} ... {root}/{maximum}/{minimum/
{y-intercept}/{intersections of two graphs}
•{Y-CAL}/{X-CAL}/{
∫
dx} ... {y-coordinate for a given x-coordinate}/{x-coordinate
for a given y-coordinate}/{integral for a given range}
145
9-2 Analyzing a Function Graph
The following two graphs are used for all of the examples in this section, except
for the example for determining the points of intersection for two graphs.
Memory location Y1 = x+ 1 Y2 = x(x+ 2)(x– 2)
Use the View Window to specify the following parameters.
(A) Xmin = –5 Ymin = –5 (B) Xmin = –6.3 Ymin = –3.1
Xmax = 5 Ymax = 5 Xmax = 6.3 Ymax = 3.1
Xscale = 1 Yscale = 1 Xscale = 1 Yscale = 1
kk
kk
kDetermining Roots
Example To determine the roots for y= x(x+ 2)(x– 2)
View Window: (B)
!5(G-Solv)
1(ROOT)
(This puts the unit into standby waiting
for selection of a graph.)
•A“k” cursor appears on the graph that has the lowest memory area number.
Specify the graph you want to use.
c
• Use fand cto move the cursor to the
graph whose roots you want to find.
Determine the root.
w
• Roots are found starting from the left.
146
Search for the next root to the right.
e
• If there is no root to the right, nothing
happens when you press e.
e
• You can use dto move back to the left.
• If there is only one graph, pressing 1(ROOT) directly displays the root
(selection of the graph is not required).
• Note that the above operation can be performed on rectangular coordinate
(Y=) and inequality graphs only.
kk
kk
kDetermining Maximums and Minimums
Example To determine the maximum and minimum for y= x(x+ 2) (x– 2)
View Window: (A)
!5(G-Solv)
2(MAX)
(This puts the unit into standby waiting
for selection of a graph.)
Specify the graph and determine the maximum.
cw
9 - 2 Analyzing a Function Graph
147
Specify the graph and determine the minimum.
!5(G-Solv)
3(MIN) cw
• If there is more than one maximum/minimum, you can use dand eto move
between them.
• If there is only one graph, pressing 2(MAX) / 3(MIN) directly displays the
maximum/minimum (selection of the graph is not required).
• Note that the above operation can be performed on rectangular coordinate (Y=)
and inequality graphs only.
kk
kk
kDetermining y-intercepts
Example To determine the y-intercept for y= x+ 1
View Window: (B)
!5(G-Solv)
4(Y-ICPT)
(This puts the unit into standby waiting
for selection of a graph.)
Determine the y-intercept.
w
•y-intercepts are the points where the graph intersects the y-axis.
• If there is only one graph, pressing 4(Y-ICPT) directly displays the
y-intercepts (selection of the graph is not required).
• Note that the above operation can be performed on rectangular coordinate
(Y=) and inequality graphs only.
Analyzing a Function Graph 9 - 2
148
kk
kk
kDetermining Points of Intersection for Two Graphs
Example To draw the following three graphs and then determine the
points of intersection for the Graph Y1 and Graph Y3.
View Window: (A)
Y1 = x+ 1
Y2 = x(x+ 2) (x– 2)
Y3 = x2
!5(G-Solv)
5(ISCT)
(This puts the unit into standby waiting
for selection of a graph.)
Specify Graph Y1.
w
• Pressing wchanges “ k” into “ ◆” for
specification of the first graph.
Specify the second graph (Graph Y3, here) to determine the points of intersection.
cw
• Use fand cto move “ k” on the
second graph.
• Intersections are found starting from the left.
e
• The next intersection to the right is found. If
there is no intersection to the right, nothing
happens when you perform this operation.
• You can use dto move back to the left.
• If there are only two graphs, pressing 5(ISCT) directly displays the intersec-
tions (selection of the graph is not required).
• Note that the above operation can be performed on rectangular coordinate (Y=)
and inequality graphs only.
9 - 2 Analyzing a Function Graph
149
kk
kk
kDetermining a Coordinate (xfor a given y/yfor a given x)
Example To determine the y-coordinate for x= 0.5 and the x-coordinate
for y= 3.2 in the graph y= x(x+ 2) (x– 2)
View Window: (B)
!5(G-Solv)6(g)1(Y-CAL)
Specify a graph.
cw
• At this time, the unit waits for input of an
x-coordinate value.
Input the x-coordinate value.
a.f
Determine the corresponding y-coordinate value.
w
Specify a graph.
!5(G-Solv)6(g)
2(X-CAL) cw
• At this time, the unit waits for input of a
y-coordinate value.
Input the y-coordinate value.
d.c
Determine the corresponding x-coordinate value.
w
Analyzing a Function Graph 9 - 2
150
9 - 2 Analyzing a Function Graph
• If there is more than one x-coordinate value for a given y-coordinate value or
more than one y-coordinate value for a given x-coordinate value, use eand
dto move between them.
• The display used for the coordinate values depends on the graph type as
shown below.
• Polar Coordinate Graph
• Parametric Graph
• Inequality Graph
• Note that you can not determine a y-coordinate for a given x-coordinate with a
parametric graph.
• If there is only one graph, pressing 1(Y-CAL) / 2(X-CAL) directly displays
the x-coordinate/y-coordinate (selection of the graph is not required).
kk
kk
kDetermining the Integral for Any Range
Example
∫
–1.5
0
x(x+ 2) (x– 2) dx
View Window: (A)
!5(G-Solv)6(g)
3(∫dx)
(Graph selection standby)
Select graph.
cw
• The display is prompting input of the lower limit
of the integration range.
Move the pointer and input the lower limit.
e~ew
151
Input the upper limit and determine the integral.
e~e(Upper limit; x= 0)
w
• The lower limit must be less than the upper limit when specifying the integration
range.
• Note that the above operation can be performed on rectangular coordinate (Y=)
graphs only.
kk
kk
kGraph Solve Precautions
• Depending on the View Window parameter settings, there may be some error
in solutions produced by Graph Solve.
• If no solution can be found for any of the above operations, the message “Not
Found” appears on the display.
• The following conditions can interfere with calculation precision and may make
it impossible to obtain a solution.
— When the solution is a point of tangency to the x-axis.
— When the solution is a point of tangency between two graphs.
Analyzing a Function Graph 9 - 2
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