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

# How to Evaluate Functions with TI-83/84

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).

## 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. 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.

## 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.”

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.

## 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. 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`.