Determining the roots of an equation using the TI 89:
Press these buttons, For this result:
ON Turn the calculator on.
, F1 Press the green diamond button and then the green 'Y='
to open the function list for entering a function.
4X^3 – X^3 Enter the expression . Do not use the purple
'alpha' button for this, the 'X' variable is 2 buttons below
the green diamond.
, F3 Press the green diamond and then the 'GRAPH' button to
graph the function.
F2 , 6 Set the viewing window to the standard [-10 x 10] for
both axes. You may need to 'Zoom' out to catch the roots
of other functions.
F5, 2 Select 'MATH' and 'ZERO' and the screen prompt us
with 'Lower Bound?'
, ENTER Move the cursor to the left of the chosen root.
And the screen prompts us with 'Upper Bound?'
, ENTER The x and y coordinates for the root are given at the
bottom of the screen.
F5, 2 Repeat the process to find the coordinates of another root.
Evaluating an equation with the table function of the TI 89:
Press these buttons, For this result:
ON Turn the calculator on.
, F1 Open the function list by pressing the green diamond and
the green Y = key and prepare to enter a function.
4/3*2nd ^X^3, ENTER Enter the equation for the volume of a sphere:

, F4 Press the green diamond and the green 'Tblset' keys to
set up the inputs and intervals for the data table.
0 , , 1, ENTER Enter the starting value of 0 and move the cursor down
to enter the number '1' for the interval between each
successive input.
, F5 Press the green diamond and the green 'TABLE' keys to
get the corresponding output for the table input values.

Note: The Absolute value function, abs(x), can be created by pressing the following keys: 2nd , ALPHA, A, B, S, ALPHA, (, X, ).

Entering Piece-wise Functions on the TI 89:
Press these buttons, For these results:
ON Turn the calculator on.
, F1 Press the green diamond and the green ‘Y =’ key
and prepare to enter the piece-wise function of f(x).

2nd , alpha, w,h,e,n, alpha, ( , X, 2nd , >, 4, X, ^, 2, -, 15, 3, X, -, 5, ), ENTER
Enter the word 'when' at the function entry list by
putting the calculator in alpha-lock and pressing
the corresponding keys beneath each purple letter.
Take the calculator out of alpha lock and then enter
the piece-wise function and its restrictions within
parentheses so that it looks like the following on
the entry line:
when( x > 4, , 3x-5)
The second restriction of '' is not entered
because the calculator accepts that the equation of
y = 3x – 5 will be used whenever the restrictions of
the first equation of have not been
met. The inequalities of '<' and '>' can be found on
the bottom rows of keys.
, F3 Graph the function by pressing the green diamond
and 'GRAPH'.
The graph is not quite right though, because there
should not be a connecting segment between the
two pieces of the function. To make sure that
piece-wise functions are graphed without any
incorrect connections, the calculator must be put
into a 'DOT' mode. Let's do that with our existing
piece-wise function.
, F1, , F4 Return to the Equation list and deselect the piece-
wise function.
2nd, F1, 2, ENTER, ENTER Change the plotting to 'Dot' mode and then select
the piece-wise function.
, F3 Graph the piece-wise function and now we can see
the jump discontinuity at x = 4.