User manual - Chapter 9 Graph Solve

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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 (y for 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

9-3 Graph Solve Precautions

Chapter

Summary of content (10 pages)

PAGE 1
Chapter Graph Solve You can use any of the following methods to analyze function graphs and approximate results.
PAGE 2
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 1 2 3 4 5 6 2 (MAX) ....... Maximum 3 (MIN) ........ Minimum 4 (Y-ICPT) ... y-intercept 5 (ISCT) ...... Intersections of two graphs 6 (g) ........... Next menu 6(g) 1 2 3 4 5 6 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) ...........
PAGE 3
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) Ymin = –3.1 Xmax = 5 Ymax = 5 Xmin Xmax = = –6.3 6.3 Ymax = Xscale = 1 Yscale = 1 Xscale = 1 Yscale = 3.
PAGE 4
9-2 Analyzing a Function Graph 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 d to 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.
PAGE 5
Analyzing a Function Graph 9-2 !5(G-Solv) 1 2 3 4 5 6 Specify the graph and determine the minimum. 3(MIN) cw • If there is more than one maximum/minimum, you can use d and e to 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.
PAGE 6
9-2 Analyzing a Function Graph k Determining 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) 1 2 3 4 5 6 5(ISCT) (This puts the unit into standby waiting for selection of a graph.) Specify Graph A. w • Pressing w changes “ k ” into “ ◆ ” for specification of the first graph.
PAGE 7
Analyzing a Function Graph 9-2 • Note that the above operation can be performed on rectangular coordinate (Y=) and inequality graphs only. k Determining a Coordinate ( x for a given y/y for 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 2 3 4 5 6 1(Y-CAL) Specify a graph. cw • At this time, the unit waits for input of an xcoordinate value. Input the x-coordinate value. a.
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9-2 Analyzing a Function Graph Specify a graph. 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 • 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 e and d to move between them. • The display used for the coordinate values depends on the graph type as shown below.
PAGE 9
Analyzing a Function Graph 9-2 k Determining the Integral for Any Range Example ∫ 0 –1.5 x (x + 2) (x – 2) dx View Window: (A) !5(G-Solv)6(g) 1 2 3 4 5 6 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 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.
PAGE 10
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.