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Shade between Functions on the TI-83 Plus

Regardless what mode the TI-83 Plus graphing calculator is in, you can shade only between functions written specifically as functions of the independent variable x. These functions don’t have to be entered in the calculator ahead of time. When you shade the area between two functions, you can shade the whole area or just a portion of that area. To shade functions, follow these steps:

  1. Press [2nd][PRGM][7] to select the Shade option from the Draw menu.

  2. Enter the definitions of the lower function, press [,], and then enter the definition of the upper function.

    The order in which you enter the functions determines what portion of the graph will be shaded. In the second picture shown, the lower function is Y1 and the upper function is Y2. In the third picture in this figure, Y2 is the lower function.

    If your calculator is in Function mode and you have already entered the functions in the calculator, then you can enter them into the Shade command by using their function names. To do so, press

    image0.png

    to open the Variables Function menu. Then press the number of the function you want to enter in the Shade command.

    If you haven’t entered the functions in the calculator (or the calculator isn’t in Function mode), enter the function definitions in the Shade command. For example, the first picture is equivalent to Shade(x2 – 1, x + 1). In parametric, polar, or sequence mode, you enter the letter x into the calculator by pressing

    image1.png image2.jpg

    If you’re shading the whole area between two functions and you like the default shading, then after completing Step 2, press [ ) ][ENTER] and skip the remaining steps.

  3. Press [,].

  4. Enter the minimum value of x in the shaded area, press [,], and then enter the minimum value of x in the shaded area.

    The minimum and maximum values of x must be between Xmin and Xmax in the Window editor. If they are not, you won’t see the total shaded area on the calculator.

    If you’re shading a portion of the area between two functions you defined in Step 4, and you like the default shading, then press [ ) ][ENTER] and skip the remaining steps.

  5. Press [,].

  6. Enter a number, 1 through 4, of the type of shading you want, and then press [.].

    Enter 1 for vertical line shading, 2 for horizontal line shading, 3 for negatively sloping diagonal line shading, or 4 for positively diagonal line shading.

  7. Enter a number from 1 through 8 to set the resolution of the shading, and then press [ ) ].

    If you enter 1, every pixel on the screen is shaded. If you enter 2, every other pixel is shaded, and so on. My favorite number for the resolution is 4, which shades every fourth pixel.

  8. Press [ENTER] to shade the graph.

    image3.jpg
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