Some Special Piecewise Linear Functions on Your TI-83 Calculator

Four special piecewise linear functions can be found on a menu in your calculator. These are the absolute value function abs that finds the absolute value of a number, and three different step functions—int finds the greatest integer less than or equal to a number (the floor function), iPart gives the integer part of a decimal number (the truncation function), and the round function can be used to round a number to the nearest integer.

Thus, abs(-1.3) = 1.3 int(2.7) = 2 int(-2.7) = -3 iPart(2.7) = 2 and round (2.7, 0) = 3.

( This last function says round 2.7 to 0 decimal places.)

To evaluate any of these functions, do the following:

• Make sure you are on the home screen.
• Press the MATH key, to get the math menu.
• Use the right cursor to highlight NUM.
• To evaluate the absolute value function at a number (or a stored list), press 1. You will see abs( on the home screen. Type in the value to be evaluated, and then ) ENTER.
• To evaluate the round function at a number (or a stored list), press 2. You will see round( on the home screen. Type in the value to be evaluated, and then , 0 then ) ENTER.
• To evaluate the integer Part function at a number (or a stored list), press 3. You will see iPart( on the home screen. Type in the value to be evaluated, and then ) ENTER.
• To evaluate the greatest integer function at a number (or a stored list), press 5. You will see int( on the home screen. Type in the value to be evaluated, and then ) ENTER.

Press the Y= key. Then, as above, Press the MATH key, to get the math menu.

Use the right cursor to highlight NUM.

Select the function you wish from the list by pressing the correct number. This puts the selected function in the Y= list, followed by a parentheses ( . Fill in the variable or variable expression, close the parentheses ), and press ENTER. [For Round, fill in the variable expression then , 0 ) ]

To graph, first set your WINDOW (if not already set), then press the MODE key. Use the cursor to go to the fifth line and highlight Dot, and press ENTER.

Now press the GRAPH key.
 
 

Exercises:

1. Evaluate each of the four piecewise linear functions at the following numbers: -5.6, 2.3, 0

2. Graph each of the four functions abs(X), round(X,0), iPart(X), and int(X) (only one at a time) for the Window

[-5 , 5] x [-5, 5]. The last three functions look a lot alike; describe how their graphs differ. Look closely at the placement of the steps in relation to the unit marks on the x-axis.