Introduction to Algebra using the TI-92 Ó 1997
by Nathan O. Niles
Associate Professor (Retired)
U. S. Naval Academy

3. Table of Values

We will illustrate the use of the TI-92 Graphing Calculator to construct a table of values of a function. There are six keys used in constructing tables and drawing graphs. They are located above the QWERTY keys and are designated by: HOME (displays results), Y= (Y editor where functions are defined and edited), WINDOW (for setting parameters for graphing), GRAPH (for displaying graphs), TblSet (for setting parameters for tables), TABLE (for displaying tables). These keys are used in conjunction with the ‘diamond key’ .

Example. Construct a table of values and then plot the points to draw the graph of f(x) = x2 - 5x + 1. Use the interval [- 1, 6]. When does the function increase and when decrease? Estimate the minimum value of f(x). When is the function zero?

Solution: A table of values is obtained as follows:

The function must be entered in the Graph Mode:   1 

Display the Y= Editor:   and clear it:  8  

 The entry line should now display y1(x)= where the cursor is flashing after the = sign. y1(x) denotes the first function, y2(x) the second function, etc. Enter the function: x  2  5x  1  At the top of the display screen you should have:  y1=x2 - 5× x + 1 (The  indicates the function that will be displayed.)

Next we enter the table parameters in the TABLE SETUP dialog box: tblStart (where the table is to start), D tbl (the increment for x), Graph < - > Table Off or On ( Off for table only), Independent Auto (automatic) or Ask ( user supplies values).

  (displays TABLE SETUP box) We want to start at x = - 1: tblStart:   1  For now lets have the values of x increase by 1: D tbl:  1  We want the table only: Graph < - > Table: OFF ®  1  We want the automatic generation of the table: Independent: AUTO ®  1 

To display the table:  

 The display should show the following table:

(Press  several times. Does the table scroll up? Press  several times. What happens? Press  and . What happens?) Press the cursor pad to return to the table where the first entry of x is - 1.

Draw a rectangular coordinate system with the same size units on both axes. Plot the points and draw the graph. You should obtain something like what appears in the figure below.

Note that f (x), here denoted as y1, decreases from x = - 1 to x = 2 and increases from x = 3 to x = 6. To estimate the minimum, note from the table that y1 = - 5 at both x = 2 and 3. To narrow this down, list a new table for [2, 3] with a spacing of 0.1.   Let tblStat: = 2 and D tbl: = .1 Then note the minimum value is - 5.25 at x = 2.5.

The function will be zero when y1 = 0 or when there is a sign change in y1. Press  repeatedly until you locate a change in sign of y1. Did you find it at x = 0.2 and x = 0.3 ? The function is zero at approximately x = 0.2. Find another sign change by pressing  repeatedly. Did you find it at x = 4.8 and x = 4.9? The function is zero at approximately x = 0.2 and 4.8. (Holding down  while pressing  will scroll the table down one page at a time. Similarly for  .) You may obtain a better approximation by listing a new table for [0.2, 0.3] with an increment of 0.01. Also a table for [4.8, 4.9] with an increment of 0.01.

Problem. Construct a table of values and plot the points to draw a graph of f (x) = - x2 + 3x + 3. (Start with the interval [- 2, 5].) When does the function increase and when decrease? Estimate the maximum value of f(x). When is the function zero? Does the function have a minimum?
 
 To Table of Contents   To Section 2. Evaluation of a function   To Section 4. Graphs of functions