Interactive Manual › Chapter 7

Chapter 7: Tables

Evaluate your Y= functions at a list of X values: set up the table with TblStart, ΔTbl and the Auto/Ask options, define and edit dependent variables, then scroll the table and change its step.

Getting Started: Roots of a Functionp. 115

A table shows the value of a function at evenly spaced X values, so it is a quick way to spot where the function crosses zero. In this example you evaluate Y = X³ − 2X at every integer from ⁻10 to 10, then look for the places where the sign of Y flips.

Tutorial

Find the sign changes of Y₁ = X³ − 2X

You will enter the function, set up the table to start at ⁻10 with a step of 1, and scroll down to find the roots.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the MODE screen and choose Func graphing. Move down three rows to the graphing-mode row, then press ENTER on Func. (It is already the default, so this just makes sure.)
MODE▼︎▼︎▼︎ENTER
Open the Y= editor.
Y=
Type X³ by pressing X,T,θ,n and then choosing 3:³ from the MATH menu. Then press − 2 X,T,θ,n to finish Y₁=X³−2X.
X,T,θ,nMATH3−2X,T,θ,n
Open the TABLE SETUP screen.
2ndTBLSET
Set TblStart=⁻10. Use (−) for the negative sign, not −.
(−)10ENTER
Set ΔTbl=1. The cursor then drops to the Indpnt row.
1ENTER
Press ENTER on Indpnt: Auto so that X values are generated for you. Then move down and press ENTER on Depend: Auto so that the Y values are calculated for you.
ENTER▼︎ENTER
Display the table.
2ndTABLE
Scroll down with ▼︎ until you can see the values of Y₁ change sign. The table shows seven rows, so the first six presses move the cursor to the bottom row and every press after that scrolls; 14 presses bring X=⁻2 to the top.
▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎
Read the answer. Y₁ is ⁻4 at X=⁻2 and 1 at X=⁻1, so the sign changes between ⁻2 and ⁻1. Y₁ is exactly 0 at X=0, with 1 before it and ⁻1 after it, which is a second sign change. Y₁ is ⁻1 at X=1 and 4 at X=2, so there is a third change between 1 and 2. That is three sign changes in all, one for each root of the function.
To look closer, press + and type a smaller step such as .5, then ENTER. Searching X in steps of 0.5 narrows down where the roots sit.
+.5ENTER

Note When the table first appears, the entry line reads Press + for ΔTbl. It is a reminder that + lets you change ΔTbl from inside the table. The message disappears as soon as you press any key.

Setting Up the Tablep. 116

Everything about how the table is built is set on one screen, TABLE SETUP. It decides where the X values start, how far apart they are, and whether the calculator or you supplies the X values and the Y values.

TABLE SETUP Screenp. 116

Press 2ndTBLSET to open the TABLE SETUP screen. It has two number fields and two option rows.

TABLE SETUP
TblStart=0
ΔTbl=1
Indpnt: Auto Ask
Depend: Auto Ask

The TABLE SETUP screen with its default settings.

Setting	What it controls
TblStart	The first value of the independent variable. It only matters while the independent variable is generated automatically (`Indpnt: Auto`).
ΔTbl	The table step: the amount added to the independent variable from one row to the next.

Tutorial

Set TblStart and ΔTbl

Make a table that starts at ⁻3 and steps by 0.5.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open TABLE SETUP.
2ndTBLSET
Type the new start value and press ENTER. The cursor moves on to ΔTbl.
(−)3ENTER
Type the new step and press ENTER.
.5ENTER
Show the table. The first rows are X=⁻3, ⁻2.5, ⁻2 and so on.
2ndTABLE

Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Askp. 116

The bottom two rows of TABLE SETUP each have two choices, Auto and Ask. Move to the row you want, highlight the choice with ◀︎ or ▶︎ and press ENTER. The four combinations behave like this.

Selections	Table characteristics
Indpnt: Auto, Depend: Auto	The calculator fills in the X column and the Y column(s) for you.
Indpnt: Ask, Depend: Auto	The table starts empty. Each X value you type gets all its Y values calculated and shown at once.
Indpnt: Auto, Depend: Ask	The X column fills in automatically. A Y value appears only when you move the cursor to its cell and press `ENTER`.
Indpnt: Ask, Depend: Ask	The table starts empty. Type the X values yourself, then move to each Y cell and press `ENTER` to calculate it.

Tutorial

Type your own X values (Indpnt: Ask)

With Indpnt: Ask, the table is blank until you enter X values.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open TABLE SETUP and move down to the Indpnt row.
2ndTBLSET▼︎▼︎
Move onto Ask and press ENTER to select it.
▶︎ENTER
Show the table. It is empty because you have not given it any X values yet.
2ndTABLE
Type an X value and press ENTER. The Y₁ value appears next to it, and the cursor moves to the next row.
3ENTER
Enter another X value. Any value works, including decimals and negatives.
(−)1.5ENTER

Tutorial

Calculate Y values on request (Depend: Ask)

With Depend: Ask, the X values appear but the Y cells stay blank until you ask for them.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open TABLE SETUP and move down to the Depend row.
2ndTBLSET▼︎▼︎▼︎
Move onto Ask and press ENTER to select it.
▶︎ENTER
Show the table. The X column is filled in, but the Y₁ column is blank.
2ndTABLE
Move the cursor right into the Y₁ column, then down to the row for X=2.
▶︎▼︎▼︎
Press ENTER to calculate Y₁ for that row. Only that cell fills in.
ENTER

Setting Up the Table from the Home Screen or a Programp. 116

The table variables can be changed without opening TABLE SETUP. Press VARS, open 6:Table…, and pick the variable name; then store a value into it like any other variable. TblInput is a read-only list holding the independent-variable values that are currently in the table (the X values you typed when Indpnt is Ask).

In the program editor, 2ndTBLSET opens a menu of four commands that set the two table options: IndpntAuto, IndpntAsk, DependAuto and DependAsk. They do exactly what the matching choices on TABLE SETUP do.

TblStart

value→TblStart

System variable holding the first independent-variable value of the table. It only has an effect when Indpnt is Auto. Scrolling the table up or down updates it.

Keys: VARS61

⁻3→TblStart makes the table begin at X=⁻3.

ΔTbl

value→ΔTbl

System variable holding the table step, the increment between consecutive independent-variable values.

Keys: VARS62

.5→ΔTbl makes the table step by 0.5.

TblInput

TblInput

A list of the independent-variable values entered in the table. It is what the table uses when Indpnt is set to Ask.

Keys: VARS63

IndpntAuto

IndpntAuto

Program command: the independent variable is generated automatically from TblStart and ΔTbl (same as choosing Indpnt: Auto).

IndpntAsk

IndpntAsk

Program command: the table waits for you to type independent-variable values (same as choosing Indpnt: Ask).

DependAuto

DependAuto

Program command: the dependent-variable values are calculated automatically (same as choosing Depend: Auto).

DependAsk

DependAsk

Program command: each dependent-variable value is calculated only when you press ENTER on its cell (same as choosing Depend: Ask).

Tutorial

Store a value to TblStart from the home screen

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Type the value and the store arrow.
5STO►
Press VARS and choose 6:Table… to open the VARS TABLE menu.
VARS6
Choose 1:TblStart. Its name is pasted after the arrow.
1
Press ENTER to store it. The table will now start at X=5.
ENTER

Defining the Dependent Variablesp. 117

The dependent variables are simply your Y= functions. Which ones appear, and how they are named, depends on the current graphing mode.

Defining Dependent Variables from the Y= Editorp. 117

Enter the functions you want in the Y= editor (press Y=). The table only shows functions that are selected, meaning the = sign after the name is highlighted. Switch a function on or off by moving onto its = sign and pressing ENTER.

The table follows the current graphing mode. In Par mode every parametric equation needs both parts defined (for example X₁T and Y₁T), as described in Chapter 4.

Editing Dependent Variables from the Table Editorp. 117

You can change a function without leaving the table. The same steps also let you read a function’s formula while looking at its values.

Press 2ndTABLE to show the table, then press ▶︎ or ◀︎ to put the cursor in a dependent-variable column.
Press ▲︎ until the cursor sits on the function name at the top of the column. The formula appears on the bottom line.
Press ENTER. The cursor moves to the bottom line, where you can edit the formula.
Press ENTER or ▼︎. The new values are calculated, and the table and the Y= function are both updated.

Tutorial

Edit a function from the table

Change Y₁=X² into Y₁=X²+1 without going back to the Y= editor.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

The table is showing. Move into the Y₁ column.
▶︎
Move up onto the column heading Y1. The formula Y1=X² is shown on the bottom line.
▲︎
Press ENTER to move the cursor to the bottom line.
ENTER
Add +1 to the end of the formula.
+1
Press ENTER to store the new formula. The column recalculates, and Y₁ in the Y= editor is updated too.
ENTER

Displaying the Tablep. 118

Press 2ndTABLE (TABLE) to see the table.

The Tablep. 118

The first column holds the independent variable. The next two columns hold the dependent variables of the first two selected functions. The bottom line shows the full, unabbreviated value of the highlighted cell, which is useful because the narrow columns shorten long numbers.

X     Y1    Y2
0     0     3
1     1     4
2     4     5
3     9     6
4     16    7
5     25    8
Press + for ΔTbl

A table in Func mode with Y1 and Y2 selected. The cursor is on the first X value, so the bottom line gives its full value.

Note When the table first appears, the message Press + for ΔTbl is on the entry line to remind you that + changes ΔTbl at any time. It disappears when you press any key.

Tutorial

Display the table for two functions

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Press 2ndTABLE to display the table.
2ndTABLE
Move down to the row for X=3. The bottom line shows the full value of the selected cell.
▼︎▼︎▼︎

Independent and Dependent Variablesp. 118

The variables shown depend on the graphing mode chosen on the MODE screen (Chapter 1). For example, Func mode shows X together with Y1 and Y2.

Graphing mode	Independent variable	Dependent variable
Func (function)	X	Y1 through Y9, and Y0
Par (parametric)	T	X1T/Y1T through X6T/Y6T
Pol (polar)	θ	r1 through r6
Seq (sequence)	n	u(n), v(n), and w(n)

Clearing the Table from the Home Screen or a Programp. 118

On the home screen, paste ClrTable from the CATALOG (2ndCATALOG) and press ENTER. In a program, choose 9:ClrTable from the PRGM I/O menu, or paste it from the CATALOG; the table is cleared when the program reaches that line.

What gets cleared depends on your setup. With IndpntAsk selected, every independent and dependent value in the table is removed. With DependAsk selected, the dependent values are removed.

Tutorial

Clear the table from the home screen

Suppose the table is in Indpnt: Ask mode and already holds three X values. ClrTable wipes them.

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the CATALOG and press ALPHAALPHAC to jump to the entries that start with C.
2ndCATALOGALPHAC
Press ▼︎ 14 times to reach ClrTable.
▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎▼︎
Press ENTER to paste ClrTable on the home screen.
ENTER
Press ENTER again to run it. The table’s X values are cleared.
ENTER

ClrTable

ClrTable

Clears the values in the table. If Indpnt is Ask, it clears all independent and dependent values. If Depend is Ask, it clears the dependent values.

Scrolling Independent-Variable Valuesp. 119

When Indpnt is Auto, press ▲︎ or ▼︎ in the independent-variable column to reveal more rows. The dependent values for the new rows are shown with them. With Depend set to Ask, some of those cells may stay blank until you request them.

Note You can scroll back past the TblStart you entered. TblStart is updated automatically to the X value on the top row. With TblStart=0 and ΔTbl=1 the table shows X=0 through 6, but pressing ▲︎ reveals X=⁻1, …, 5.

Tutorial

Scroll back before TblStart

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

The table starts at X=0. Press ▲︎ to scroll back.
▲︎
Press ▼︎ seven times: six presses take the cursor down to the bottom row, and the seventh scrolls the table forward. TblStart follows the top row.
▼︎▼︎▼︎▼︎▼︎▼︎▼︎

Changing Table Settings from the Table Viewp. 119

With the cursor on any value in the independent-variable column, press + and type a new ΔTbl. In the example below you enter Y₁=½X, move to the X=3 row, and change the step to ½ so the table shows X=3, 3.5, 4 and so on.

Tutorial

Change ΔTbl to 1/2 from the table

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the Y= editor and enter Y₁=1/2X: type 1, divide by 2, then X,T,θ,n.
Y=1÷2X,T,θ,n
Display the table.
2ndTABLE
Move down three rows to highlight X=3.
▼︎▼︎▼︎
Press +. The bottom line now asks for ΔTbl.
+
Type the new step, 1/2, and press ENTER.
1÷2ENTER

Displaying Other Dependent Variablesp. 120

If more than two functions are selected, the table starts with the first two. Press ▶︎ or ◀︎ to scroll across to the others. The independent variable stays in the left column, except during a trace in Par mode with G-T split screen.

Tip To see two functions side by side that are not consecutive, deselect the ones between them in the Y= editor. For example, to compare Y4 and Y7, deselect Y5 and Y6.

Tutorial

Show Y4 and Y7 together

▶ Try this step-by-step on the online TI-84 Plus — keys light up as you go

Open the Y= editor and move down to Y₅.
Y=▼︎▼︎▼︎▼︎
Move left onto the = sign and press ENTER to deselect Y₅. Then press ▼︎ and ENTER to deselect Y₆.
◀︎ENTER▼︎ENTER
Show the table, which starts with the first two selected functions, Y1 and Y2.
2ndTABLE
Press ▶︎ repeatedly to scroll across the selected functions. After five presses the cursor is in the Y7 column, directly beside Y4, because Y5 and Y6 are skipped.
▶︎▶︎▶︎▶︎▶︎
Press ◀︎ to move back to the Y4 column.
◀︎

1:TblStart	The starting value of the independent variable.
2:ΔTbl	The step between independent-variable values.
3:TblInput	The list of independent-variable values currently in the table.