TI-83 Tutorial

Finding Values of a Function

The first goal is to illustrate one procedure for evaluating a function by storing the function f(x) = x3 - 2x + 1 in memory, and then finding f(1.003).


Use the key to get to the function editor, so that you can enter the function.

Step 1

Enter the function y1 = x3 - 2x + 1.
On your calculator, the entry for Y1 in the function editor should look like this:
     ________________________________
    |                                |
    | Y1=X^3-2X+1                    |
    | Y2=                            |
    | Y3=                            |
    | Y4=                            |
    | Y5=                            |
    |                                |
    |                                |
    |                                |
    |                                |
    |________________________________|

Step 2

Set x = 1.003. To do this, you must store the value 1.003 in the variable X, and this is done by entering 1.003 followed by the keystrokes .
Your screen should look like this:
     ________________________________
    |                                |
    | 1.003->X                       |
    |                         1.003  |
    |                                |
    |                                |
    |                                |
    |                                |
    |                                |
    |                                |
    |                                |
    |________________________________|

Step 3

Call up the function Y1. This is done by using the key. You should see the screen shown below.
     ________________________________
    | VARS  Y-VARS                   |
    | 1:Function...                  |
    | 2:Parametric...                |
    | 3:Polar...                     |
    | 4:On/Off                       |
    |                                |
    |                                |
    |                                |
    |                                |
    |                                |
    |________________________________|
Use your cursor key (move to the right) to highlight Y-VARS, and then press the key. Now the screen should look like this:
     ________________________________
    | FUNCTION                       |
    | 1:Y1                           |
    | 2:Y2                           |
    | 3:Y3                           |
    | 4:Y4                           |
    | 5:Y5                           |
    |                                |
    |                                |
    |                                |
    |                                |
    |________________________________|
The 1 should be highlighted, and since this is the function you want, just press key.
Here is the way the screen should look.
     ________________________________
    |                                |
    | 1.003->X                       |
    |                         1.003  |
    | Y1                             |
    |                                |
    |                                |
    |                                |
    |                                |
    |                                |
    |                                |
    |________________________________|

Step 4

A final press of the key gives you the value of Y1 that corresponds to the value of X in calculator's memory.
     ________________________________
    |                                |
    | 1.003->X                       |
    |                         1.003  |
    | Y1                             |
    |                    .003027027  |
    |                                |
    |                                |
    |                                |
    |                                |
    |                                |
    |________________________________|


Using Values of a Function in Other Calculations

You may have learned to evaluate a function by graphing it and then using the TRACE button. One advantage of the method presented above is that you can evaluate more complicated expressions involving the function. By calling up Y1 in the same way you did before, you can evaluate expressions like the following difference quotient

.

Remember that the function is f(x) = x3 - 2x + 1. Computing by hand you get f(2) = 5. As is typical with a difference quotient, we want to see what we will get for some values of x close to 2.
     ________________________________
    |                                |
    | 2.01->X                        |
    |                          2.01  |
    | Y1                             |
    |                      5.100601  |
    | (Y1-5)/(X-2)                   |
    |                       10.0601  |
    |                                |
    |                                |
    |                                |
    |________________________________|
You have more flexibility if you combine these steps into a single entry. Use the keystrokes to put a " : " between the previous entries. Now when you press the key, your screen should look like this.
     ________________________________
    |                                |
    | 2.01->X:(Y1-5)/(X-2)           |
    |                       10.0601  |
    |                                |
    |                                |
    |                                |
    |                                |
    |                                |
    |                                |
    |                                |
    |________________________________|
By entering the expression this way, you can repeat it by using the keystrokes . Now you can easily edit the expressions by using the cursor keys, and the delete and insert keys. You can change either the value of x, or the expression in Y1.
     ________________________________
    |                                |
    | 2.01->X:(Y1-5)/(X-2)           |
    |                       10.0601  |
    | 2.001->X:(Y1-5)/(X-2)          |
    |                     10.006001  |
    | 2.0001->X:(Y1-5)/(X-2)         |
    |                   10.00060001  |
    |                                |
    |                                |
    |                                |
    |________________________________|
You can also use the key to change the function, and then come back to the same screen on the calculator.


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