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Using the Accessible Graphing Calculator:
Known Problems or Tricks of the Trade

• Don’t plot less than three nor more than 1000 points.
• Be sure that your x min and x max DO NOT include values that will result in y values that are non-real numbers.
• For example, if you wish to graph y = the square root of x, you would enter sqrt(x) in the expression box, but you would also need to change the x min to “0.” The use of any negative numbers for x will result in an “invalid expression.”
• For example, if you wish to graph the circle:

  x 2 + y 2 = 4, which is not a function, you need to create two separate functions: the top of the circle and the bottom of the circle. Graph: y = sqrt(4-x^2) in Data 1 and y = -sqrt(4-x^2) in Data 2, but you need to be sure that your x min is –2 and your x max is 2 (the positive and negative square roots of 4).

• Solving Systems of Equations Graphically
• The AGC has a tracer function like other graphing calculators (ALT- right arrow ), which verbalizes the coordinates of each point as you trace. However, it doesn’t voice when you have reached a point of intersection for two graphs displayed at once. When graphing a system of equations (two data sets), go to the Plot Tab Page, Section “Source,” and select “Difference (1-2).” Then press Alt-0 to find the approximate x-value(s) of the point(s) of intersection. Then go to the data table of either or both equations and search for the y-value(s) associated with the x value(s) you have determined. You will now have the approximate coordinates for the point(s) of intersection (if any exist).
• Another alternative is to print the graph of the system to a Tiger graphics embosser (or print it to a print printer with Braille font, copy onto swell paper, and run through a tactile imaging machine if you don’t have a Tiger). Then determine the point(s) of intersection(s) (if any exist) from the hard copy graph.
• Unless the point of intersection is a pair of integers, graphing isn't the best method of solving systems. Even then, most graphing calculators don't give you the correct answer, only an approximation. Instead of giving you the solution of (1, 4), they might indicate (1.012, 3.998) for example.
• Solving Systems of Equations Symbolically
• Shortly after learning the graphing method, students learn how to solve systems of linear equations using substitution, linear combination, and matrices. Since the AGC will do matrices, I give you the following example.
• If you had the system:
  3x - 5y = -7
  5x - 8y = -11
  Go to the matrix tab. Type INV[3,-5;5,-8] (Note this is using the coefficients of the variables.)
  It will give you the inverse of that first matrix: [-8,5;-5,3] or something fairly close.
  Then, you would multiply that last answer by the matrix

[-7;-11] (constants on the right side of each equation) and the answer will pop out as: [1;2].
This solution matrix shows you that the answer is (1, 2) or the point of intersection.

• Quadratic-Linear and Quadratic-Quadratic Systems can also be solved symbolically.
• The AGC will not graph inequalities per se; that is, it will not shade above or below the boundary line of the inequality. When graphing a system of inequalities, you will need to graph the system of boundary equations, emboss the graphic, and manually determine the solution of the associated inequalities.
• To produce graphs with different thicknesses (and/or more than two graphs on the same page), you might want to try something that I HAD to do when the old AGC would not graph two equations at the same time. I would have the Tiger embosser take the paper back in, and I would emboss a second graph on top of the first using the exact same domain and range. However, to minimize paper perforation, at the print stage, I would eliminate everything I could – uncheck everything, no labels, no axes, no title, etc. Therefore, you can still do this and get 4 graphs (I wouldn’t do more!) on one paper. You might want to do this for certain graphs, but not for everything. (The same technique works for creating a print copy with a braille font. Still eliminate the items mentioned above, so as not to create a “blurred” copy.) To change the appearance of each separate graph, I would change the number of points plotted, and/or use the points only, line through points only, or both points and line option when printing/embossing. The results were amazing and might be helpful, especially for inequalities.
• While eliminating the axis labels, I discovered that the “instructions” were reversed. That is, if you uncheck the “X Labels,” you eliminate the “Y Labels,” and vice versa.
• You will want to take advantage of the “Title” box just before you print as well. If the student is creating the graph, they might wish to type in their name (in ASCII though to get proper braille). Since I have so many braille readers, they have to do this to distinguish their graph from the others! If the teacher is creating the graphic and the student is not supposed to know the associated equation, they might want to type in “Figure 1.”
• The Auto-Speak Coordinates Box (check box entitled “Speak X and Y values at each step”) found at the bottom of the Wave page is not voiced.
• When creating graphs of trig functions, it would sometimes be convenient to label the x-axis in terms of pi or even 90, 180, 270, 360. Unfortunately there is no toggle switch to convert your default settings to trig settings. You have to use decimal approximations for radian measures. For example: pi = 3.142; 90 = pi/2 = 1.571; etc.
• The AGC is certainly not as perfect as I would like it to be, but they continue to improve it; they really listen to us; and many of my students can and do use the AGC independently. The AGC is approved for standardized tests in Texas and elsewhere.

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Last Revision: March 24, 2005