Casio FX-9750G 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/xfor

a given y)

•Determination of the integral for any range

9-1 Before Using Graph Solve

9-2 Analyzing a Function Graph

9-3 Graph Solve Precautions

Chapter

164

9-1 Before Using Graph Solve

After using the GRAPH Mode to draw the graph, press !5(G-Solv) to display

the graph solve menu.

!5(G-Solv)

1(ROOT) .... Root

2(MAX)....... Maximum

3(MIN) ........ Minimum

4(Y-ICPT) ... y-intercept

5(ISCT) ...... Intersections of two graphs

6(g) ........... Next menu

6(g)

1(Y-CAL) .... y-coordinate for a given x-coordinate

2(X-CAL).... x-coordinate for a given y-coordinate

3(∫dx).......... Integral for a given range

6(g) ........... Previous menu

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165

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

Memory location 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.

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166

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 (selec-

tion of the graph is not required).

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

and inequality graphs only.

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.

9 - 2 Analyzing a Function Graph

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167

!5(G-Solv)

Specify the graph and determine the minimum.

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.

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 that 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.

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Analyzing a Function Graph 9 - 2

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168

kDetermining Points of Intersection for Two Graphs

Example To draw the following three graphs and then determine the points

of intersection for the Graph A and Graph C.

View Window: (A)

Graph A: y= x+ 1

Graph B: y= x(x+ 2) (x– 2)

Graph C: y= x2

!5(G-Solv)

5(ISCT)

(This puts the unit into standby waiting

for selection of a graph.)

Specify GraphA.

• Pressing wchanges “ k” into “ ◆” for speci-

fication of the first graph.

Specify the second graph (Graph C, 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).

9 - 2 Analyzing a Function Graph

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169

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

and inequality graphs only.

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.

!5(G-Solv)6(g)

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Analyzing a Function Graph 9 - 2

170

Specify a graph.

2(X-CAL) cw

• At this time, the unit waits for input of a y-coor-

dinate value.

Input the y-coordinate value.

d.c

Determine the corresponding x-coordinate value.

• If there is more than one x-coordinate value for a given y-coordinate value or

more than oney-coordinate value for a given x-coordinate value, use eand d

to 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).

9 - 2 Analyzing a Function Graph

171

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.

e~ew

Input the upper limit and determine the integral.

e~ew

• 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.

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Analyzing a Function Graph 9 - 2

172

9-3 Graph 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.

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