How to Graph a Function on a TI-84

Graphing on a TI-84 is a five-step job: open the Y= editor, type the equation, check it is switched on, press GRAPH and then read what you need from the screen. Most of the trouble students hit happens between the second step and the third, when one small detail stops the curve being drawn at all.

This page walks through the whole sequence with Y1 = 2X − 3 as the example, then explains the four reasons a graph comes up blank and how to tell them apart. It finishes with TRACE, which turns a picture into usable numbers, and with the window settings that decide how much of the shape you actually see.

If you are new to the calculator, work through it once with the example equation rather than with your homework question. A curve you already know the shape of makes each stage of the process obvious.

Step 1: enter the equation in the Y= editor

Press Y=. The editor opens with the cursor ready on the first line, and this is where the equation goes.

Type the right-hand side of the equation only. For a line through the origin with slope two and an intercept of minus three, the line reads 2X-3. The variable key is the one marked X,T,θ,n, and it inserts an X on the home screen and in graph equations.

Two details are worth knowing before you move on:

• Fractions and brackets. If the equation contains a fraction such as one third of X, enter it with the template under ALPHA Y= rather than as a decimal, so the graph is drawn from an exact value. Our guide to entering fractions covers the keystrokes.
• The minus sign. Use the small grey minus key for subtraction, not the negative-sign key. They look similar on the keypad, and the wrong one produces a syntax error or a graph of the wrong function.

Step 2: check the equation is switched on

Before pressing GRAPH, look at the equals sign beside Y1. If it is highlighted, the function is selected. If it is not, the equation will sit in the list and never be drawn, which is the single most common cause of a blank graph.

To change it, move the cursor onto the equals sign with the arrow keys and press ENTER. Pressing it again switches the function back off, which is useful when you want to keep three or four equations in the editor and view them one at a time.

The marker at the far left of the line controls the plot style. Press the left arrow until the cursor reaches it, then press ENTER repeatedly to cycle through styles: a thin line, a thick line, shading above the curve, shading below it, and an animated path. None of these change what the graph means, so leave the style alone unless a question asks you to shade a region.

Step 3: press GRAPH

Press GRAPH. The curve is drawn across the current window, with the axes and their tick marks in place.

Reading two coordinates straight away is a habit worth building. For this line, the vertical intercept at −3 and the crossing at 1.5 both come from the equation, so if the drawing does not match them, the equation on the line is not the one you meant to type.

Why the graph can come up blank

A blank graph screen has a short list of causes, and they are worth checking in this order because the first two cover almost everything.

1. The function is switched off. The equals sign beside Y1 is not highlighted. Fix it by pressing ENTER with the cursor on the equals sign.
2. The curve is outside the window. The shape is sitting above the top, below the bottom, or beyond the left or right edge. Press ZOOM and choose 6:ZStandard, which resets the view to −10 to 10 on both axes.
3. A stat plot is switched on. If Plot1 is highlighted in the Y= editor and its lists are empty or of different lengths, the calculator tries to draw the plot instead, and you may meet ERR: INVALID DIM. Move the cursor onto the plot name and press ENTER to switch it off.
4. The wrong graph mode. Press MODE and check that FUNC is selected. In POLAR, PARAMETRIC or SEQUENCE mode the Y= editor is a different editor, and equations typed for a function graph will not appear.

If the calculator refuses to draw and shows a range message instead, the window values themselves are the problem. Our guide to changing the window explains what each value does and when a preset is the fastest fix.

Step 4: read values with TRACE

A graph is only useful once you can take numbers off it. Press TRACE and a cursor appears on the curve with the coordinates of its position at the bottom of the screen.

The arrow keys slide the cursor along the curve; each press moves one screen pixel, so the values you land on depend on the current window. To go straight to a particular value, type the number and press ENTER. With several curves plotted, the up and down arrows switch between them, and the equation label at the top of the screen tells you which one you are following.

TRACE is the quickest way to answer questions of the form “use your graph to find the value of Y when X is 2.5”. For a more precise readout, or to find every crossing exactly, the search routines under 2nd TRACE are the better choice.

A quadratic example, and how the shape should look

The same five steps work for any function. Entering Y1 = X² − 2X − 3 gives a parabola, and the shape on screen carries useful information if you know what to look for.

Three features are worth reading from a parabola: the two crossings on the horizontal axis, the turning point between them, and the intercept on the vertical axis. All three can be found precisely from the CALC menu rather than estimated by eye.

If the curve looks flattened or the turning point appears as a sharp corner, that is a window problem rather than a calculator fault. Press ZOOM 4:ZDecimal for a view in which one unit of X equals a whole number of screen steps, and the symmetry of the parabola becomes clear.

Checking the picture against the numbers

The TABLE screen is the fastest cross-check on a graph you have just drawn. Press 2nd GRAPH and the calculator lists X values against the matching Y1 values, so a sign change in the column marks a crossing on the horizontal axis and the value at X = 0 gives the vertical intercept. Our guide to the TABLE feature shows how to set it up.

On test day, remember that the SAT permits a graphing calculator on all of its maths questions and the ACT permits it on the mathematics test only, in both cases with calculators that have a computer algebra system prohibited. A graph you can draw quickly and read accurately is worth real time. Our SAT calculator policy page and the summary of whether TI-84 calculators are allowed set out the conditions; rules do change, so confirm the current wording with the board.