→ TI-83/84/89 → Evaluating Functions
Updated 5 Aug 2007

Evaluating Functions with TI-83/84

Copyright © 2001–2017 by Stan Brown

Summary: Very often, you need to evaluate a function for several values of x. Examples: finding a limit or an approximation numerically, plotting on paper by plotting points. This page gives you two techniques, creating a table of values and tracing a graph. We’ll use this function to show the methods:

f(x) = (x³ − 1) / (x − 1).


See also: Graphing Functions on TI-83/84
Graphing Piecewise Functions on TI-83/84

Both Methods: Enter the Function

You have to tell the TI-83/84 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 right-hand 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.
TI-83/84 ‘Y=’ screen   TI-83/84 ‘Y=’ screen cleaned up
Enter the function. Cursor to any empty Y= slot.
Press [(] [x,T,θ,n] [^] [3] [] 1 [)] [÷] [(] [x,T,θ,n] [] 1 [)] [ENTER].

TI-83/84 Y= screen with function entered 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.

Method 1: Table of Values

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.”

TI-83/84 table setup Your top two rows may be different, but your bottom two rows will look like the screen at right. These settings tell the TI-83/84 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 TI-83/84 immediately displays the function value.

TI-83/84 Table screen

Method 2: Trace on the Graph

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.
TI-83/84 Format screen
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 an x value, then [ENTER]. You should see the function, the x value, and the y value displayed (below right).
graph of function graph of function with x and y
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.

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