How to Put Piecewise Functions Into a Graphing Calculator

Graphing calculators can store functions such as piecewise functions.

A function is an equation in which for each "x," or independent variable, in the domain, the output is just one "y," or dependent, variable value. A piecewise function is a function that changes depending on the value of the independent variable. Graphing calculators, such as the TI-89, can process piecewise functions. Once you put a piecewise function into the calculator, you can use it to display a graph or table of the function.

Instructions

1. Open the calculator’s equation editor. To do this on a TI-89, press the green diamond button and then the “F1.”

2. Enter the first function portion and first conditional portion next to “y1.” On some calculators, you may need to use a particular key sequence for entering the piecewise function. On a TI-89, before typing the function, press the “catalog” button, select “when(” and enter the conditional portion. For example, given the piecewise function f(x) = 3x + 2 when x < -2 and f(x) = x^3 when -2 <= x is entered as “when(x < -2, 3*x+3, x^3).” In the "when" statement on a TI-89, first enter the first conditional expression, then enter the function that is used if the conditional expression is true. Lastly, enter the function that is used if the conditional expression is false.

3. Enter any additional portions of the piecewise function. If there are no additional portions, go to Step 4. For example, to enter the function f(x) = 3x + 2 when x < -2 and f(x) = x^3 when -2 < x and f(x) = 5 when x = -2, another when statement is needed; enter it as “when(x < -2, 3*x+3, when(x > -2, x^3, 5)).”

4. Press “Enter.” The piecewise function is now stored in the graphing calculator.

References

• Houston Area Calculus Teachers: Using the TI Graphing Calculator on Piecewise Functions, Piecewise Derivatives, Area and Volume