Piecewise-Defined Functions on the TI-83 Plus

By C. C. Edwards

When graphing a piecewise-defined function on the TI-83 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:


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

  2. Turn off Y1, Y2, and Y3 by unhighlighting their equal signs.

    This is done in the Y= editor by using the


    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 un-highlighted. The calculator graphs a function only when its equal sign is highlighted.

  3. Enter the piecewise-defined function in Y4 as


    The function must be entered as it appears here, complete with parentheses.

    • To enter Y1, Y2, and Y3: Press


      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.