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How to Graph Piecewise-Defined Functions on the TI-84 Plus

When graphing a piecewise-defined function on the TI-84 Plus graphing calculator, some people cop out and simply graph each of the separate functions that appear in it. But this does not result in an accurate graph.

To accurately graph the following piecewise-defined function, perform the following steps:

image0.png
  1. Enter the functions Y1, Y2, and Y3 in the Y= editor.

    image1.jpg
  2. Turn off Y1, Y2, and Y3 by removing the highlight from their equal signs.

    This is done in the Y= editor by using the

    image2.png

    keys to place the cursor on the equal sign in the definition of the function and then pressing [ENTER] to toggle the equal sign between highlighted and not highlighted. The calculator graphs a function only when its equal sign is highlighted.

  3. Enter the piecewise-defined function in Y4 as

    image3.png

    The function must be entered as it appears here, complete with parentheses. (Y1)(x < a) tells the calculator to graph the function Y1 for x < a.

    • To enter Y1, Y2, and Y3: Press

      image4.png

      and then press the number of the function you want to use in the definition.

    • To enter the inequalities: Press [2nd][MATH] to access the Test menu, and then press the number of the inequality you want to use in the definition. For example, to enter the less-than (<) symbol, press [2nd][MATH][5].

  4. Press [ENTER].

  5. Graph the piecewise-defined function.

If one or more of the functions in your piecewise-defined function is a trigonometric function, make sure the calculator is in Radian and not Degree mode. Otherwise, your piecewise-defined function may look like a step function instead of the graph you were expecting.

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