Casio CFX-9850G PLUS User manual

Graph Solve

You can use any of the following methods to analyze function

graphs and approximate results.

•Calculating the root

•Determination of the local maximum value and local minimum

value

•Determination of the y-intercept

•Determination of the intersection of two graphs

•Determination of the coordinates at any point (yfor a given x/

xfor a given y)

•Determination of the integral for any range

9-1 Before Using Graph Solve

9-2 Analyzing a Function Graph

Chapter

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}/{local maximum value}/{local

minimum value}/{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

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.

•Use fand cto move the cursor to the

graph whose roots you want to find.

Determine the root.

•Roots are found starting from the left.

146

Search for the next root to the right.

•If there is no root to the right, nothing

happens when you press 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.

kDetermining Local Maximum Values and Local Minimum

Values

Example To determine the local maximum value and local minimum

value 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 local maximum value.

9 - 2 Analyzing a Function Graph

147

Specify the graph and determine the local minimum value.

!5(G-Solv)

3(MIN) cw

• If there is more than one local maximum/minimum value, you can use dand

eto move between them.

•If there is only one graph, pressing 2(MAX) / 3(MIN) directly displays the

local maximum/minimum value (selection of the graph is not required).

•Note that the above operation can be performed on rectangular coordinate (Y=)

and inequality graphs only.

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.

•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

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.

• Pressing wchanges “ k” into “ ◆” for

specification of the first graph.

Specify the second graph (Graph Y3, here) to determine the points of intersection.

•Use fand cto move “ k” on the

second graph.

•Intersections are found starting from the left.

•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

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.

•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.

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.

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).

kDetermining the Integral for Any Range

Example

∫

–1.5

x(x+ 2) (x– 2) dx

View Window: (A)

!5(G-Solv)6(g)

3(∫dx)

(Graph selection standby)

Select graph.

•The display is prompting input of the lower limit

of the integration range.

Move the pointer and input the lower limit.

d~dw

151

Input the upper limit and determine the integral.

e~e(Upper limit; x= 0)

•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.

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

152

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