How to Evaluate Functions with TI-83/84
Copyright © 2001–2023 by Stan Brown, BrownMath.com
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:
How to Graph Functions on TI-83/84
How to Graph 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. |
|
| 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.