How to Use the Table Feature on a TI-84

The TABLE screen is the quiet workhorse of the TI-84. It lists values of X beside the matching values of Y1, which makes it the fastest way to answer a question that asks for a value at a particular point, and the quickest check on a graph that you have just drawn.

It is also easy to open, see nothing, and assume the calculator is broken. Almost every empty table comes down to one of two things: the function is switched off in the Y= editor, or the start value is set so far away that the useful part of the table is off screen.

This page covers the two screens involved, the settings that decide what appears in the column, and the two jobs the table does well: finding a value and testing a graph.

Opening the table

Press 2nd and then GRAPH. The label TABLE sits above the GRAPH key for exactly this reason, and the screen that opens shows a column of X values with one or more columns of function values beside it.

Nothing appears in a function column unless that function is selected. Turn a function on or off by moving the cursor onto the equals sign in the Y= editor and pressing ENTER, which is the same switch that controls whether the curve is drawn. A function that is switched off is absent from the table as well as from the graph, which is a neat way to compare two versions of the same expression: keep both, switch one off, and the table shows only the one you are interested in.

TBLSET: the screen that decides what appears

Press 2nd and then WINDOW to open TABLE SETUP.

Four settings do all the work:

• TblStart is the first value in the x column. It applies when the x column is being generated for you.
• ΔTbl is the step between one row and the next. A step of 1 lists whole numbers; a step of 0.5 adds the halves; a negative value counts downwards.
• Indpnt decides how the x column is filled, either automatically (Auto) or by you (Ask).
• Depend decides how the function values are produced. Left on Auto they are calculated as soon as the row exists; set to Ask they are calculated one at a time as you press ENTER on a row.

The defaults of TblStart at 0, ΔTbl at 1, and both switches on Auto suit the majority of schoolwork, and they are the settings a reset puts back. Our guide to resetting a TI-84 covers what else changes.

Auto versus Ask

With Indpnt on Auto, the calculator builds the column itself, generating values evenly spaced by ΔTbl. For Y1 = 2X − 3 with TblStart at 0 and ΔTbl at 1, pressing 2nd GRAPH gives a tidy list.

Ask mode hands the column over to you. Set Indpnt to Ask and the table opens with an empty x column; type a value, press ENTER, and the calculator works out the matching Y1. This is the setting to use when the values you need are not evenly spaced.

Two habits are worth forming here. First, after a set of Ask values, the rows stay in the order you entered them rather than being sorted, so read the x column rather than assuming the sequence. Second, if you want the numbers back in order, switch Indpnt to Auto rather than retyping them.

Using the table to find a value

The table answers the question “what is Y when X is this” without any substitution. Read across the row for the X you want and take the number beside it.

It also exposes structure that a single value hides. In the Auto table above, the Y1 values rise by two for every one step in X, which tells you the gradient of the line without doing any work. A quadratic shows equal second differences in the same way, and a pattern that does not repeat at all is a sign that you are looking at something other than a polynomial.

If you have Y1 = 2X − 3 in the editor and you want the value at X = 2.5, either switch to Ask and type it, or set ΔTbl to 0.5 and let the column generate the halves for you. Both routes give Y1 = 2.

Using the table to check a graph

The second job is the more valuable one. A table is a numerical cross-check on a picture, and it catches the two mistakes that a drawing hides: a window that is cutting off part of the curve, and an equation typed differently from the one you intended.

Three checks take a few seconds each:

1. The vertical intercept. The row where X is 0 shows the value at which the curve meets the vertical axis. If the graph shows the line crossing the axis somewhere else, one of the two is wrong.
2. The sign change. Between two adjacent rows the Y1 values change from negative to positive, which means the curve crosses the horizontal axis somewhere in between. That narrows the position of a root before you search for it.
3. The height of the curve. If every table value sits far above or below the graph’s visible range, the window is cutting the curve off and needs widening.

The table can only narrow a root down, never pin it exactly, because it shows only the values you asked for. Once the sign change is between two rows a step apart, switch to the approach in our intercepts guide and use the zero routine for an exact coordinate.

Keeping the table and the graph in step

The window and the table are controlled by different screens, and changing one does not move the other. If you want the table rows to match the tick marks on your graph, set TblStart to the same value as Xmin and ΔTbl to the same value as Xscl. The window guide explains what those values do.

If the table stays stubbornly empty after all of this, the cause is usually the equation rather than the settings. A line that the calculator cannot evaluate, such as an expression with a missing bracket, produces ERR: SYNTAX when you press GRAPH and leaves the table with nothing to show. Press 2:Goto on the error screen to jump to the offending character, and the full error list covers the other messages you may meet.

In an exam

A table is a legitimate tool on paper-based exams, because it shows values you could have worked out by hand, and it takes seconds rather than minutes. The SAT permits a graphing calculator on all of its maths questions, and the ACT permits one on the mathematics test only, with calculators that have a computer algebra system prohibited in both cases. Our SAT calculator policy and ACT calculator policy pages set out the conditions, and the boards revise them from time to time, so confirm the current wording before you sit the paper.