How to Evaluate Functions with TI83/84
Copyright © 2001–2020 by Stan Brown
Copyright © 2001–2020 by Stan Brown
f(x) = (x³ − 1) / (x − 1).
See also:
How to Graph Functions on TI83/84
How to Graph Piecewise Functions on TI83/84
You have to tell the TI83/84 what your function is, before you can use Method 1 or Method 2.
If any other plots are active (highlighted), you need to
turn them off. If nothing is highlighted on your Y= screen,
you can skip this step.
It so happens that I had Plot1 and
Y2 active, as you can see below left. In the
righthand panel I’ve deactivated both of them.

Press [Y= ].
Use the blue arrow keys to move the cursor onto every highlighted = sign or Plot number, and press
[ENTER ].
Your screen will look different, but that’s okay as long as you
have nothing highlighted. 
Enter the function.  Cursor to any empty Y= slot.
Press [ ( ] [x,T,θ,n ] [^ ] [3 ] [− ] 1
[) ] [÷ ] [( ] [x,T,θ,n ] [− ] 1 [) ] [ENTER ]. 
You may be using a different function number, but make sure your entry
looks like my Y3
.
If you made a mistake, go back and edit it.
This method works strictly by numbers.
Press [2nd WINDOW makes TBLSET ].  
The first two rows don’t matter.  Press [▼ ] [▼ ] to get to the
“Indpnt” row. This controls the independent variable x.
Press [ ► ] [ENTER ] to select
“Ask.”
Press [ ▼ ] [ENTER ] to select “Depend:
Auto.” 
Your top two rows may be different, but your bottom two rows will look like the screen at right. These settings tell the TI83/84 to ask you for values of the independent variable x, then automatically calculate the values of the dependent variable f(x).
Now you can evaluate the function at selected x values.  Press [2nd GRAPH makes TABLE ].
You may see some values on the table screen. They don’t do any harm, but if you want you can get rid of them by hitting [ DEL ] several times. 
Enter the x values, one at a time. For instance, to home in on the limit as x approaches 1, we might enter .5, .75, .9, .99, and so on.  Enter each x number and press [ENTER ]. The TI83/84
immediately displays the function value. 
This method is a little more work, but you get a picture of the function. Start by entering the function on the Y= screen as shown above.
Set formatting so that the desired information will appear on your graph.  Press [2nd ZOOM makes FORMAT ].
The other settings are not critical, but you need CoordOn
and ExprOn . Press the arrow keys and [ENTER ] to
set the modes. 
Either set up the Window screen, or use “Zoom Standard” for a first look at the graph. It happens that we want the limit as x goes to 1. Since that fits within the standard window, we’ll use Zoom Standard this time.  Press [ZOOM ] [6 ] to select ZoomStd. The graph
should appear (below left).
Press [ TRACE ], then enter an .x value, then
[ENTER ]. You should see the function, the x value, and
the y value displayed (below right). 
Enter any other values, such as .99, .995, .999. The dot will move along the graph, and the new y values will be displayed.  You don’t have to press [TRACE ] again. Simply enter
each new x value, followed by [ENTER ]. 
For this function it’s not an issue, but for other functions if
your x value is outside the window, you need to press
[WINDOW
] and adjust Xmin
or Xmax
. You can only trace x
values that are between Xmin
and Xmax
.
Updates and new info: https://BrownMath.com/ti83/