TI-89GRAPHING
Graphing on the TI-89 Titanium: Functions, Circles and Inequalities
Most questions about how to graph on the TI-89 Titanium come down to three screens: the Y= editor where you type the function, the WINDOW where you set the range, and the GRAPH screen itself. This article walks through them, then shows how to graph circles on a TI-89, how inequalities are shaded, and how to read zeros and extrema from a graph.
The three graph screens: Y=, WINDOW and GRAPH
The graph screens sit on the top row as ◆ functions. ◆ F1 opens the Y= editor, ◆ F2 the WINDOW settings and ◆ F3 draws the GRAPH. ◆ F4 and ◆ F5 are TBLSET and TABLE, for a table of values.
- Press ◆ F1. The editor lists y1=, y2= and so on.
- Move to y1=, press ENTER, type the function in x and press ENTER again. A check mark means the function is selected and will be drawn.
- Press ◆ F3. If nothing useful appears, open the zoom menu on the graph screen (F2) and choose ZoomStd for the standard window from −10 to 10 on both axes.
The x key is a key of its own on the TI-89 Titanium, so you never need alpha for it. On the graph screen, F3 starts Trace: the cursor follows the curve and the bottom line shows x and y. Type a number while tracing to jump to that x value.
Reading zeros, minimum and maximum
The F5 Math menu on the graph screen finds zeros, minima, maxima and intersections. You set a lower and an upper bound around the point with the cursor, press ENTER, and the result appears on the screen. When you want the exact value, do the same on the home line with the CAS:
| Input | Result |
|---|---|
| zeros(x^2-9,x) | {−3,3} |
| fMin(x^2-4x,x) | x=2 |
| fMax(-x^2+2x,x) | x=1 |
| solve(x^2=9,x) | x=−3 or x=3 |
zeros( returns all zeros as a list, fMin( and fMax( return the x value of the minimum or maximum, and solve( handles intersections: set the two functions equal and solve for x. fMin( and fMax( are in the F3 Calc menu.
A tangent line comes from F5 Math, Tangent on the graph screen of the handheld. Calc89 also accepts tangentLine( on the home line, which gives the equation directly:
| Input | Result |
|---|---|
| tangentLine(x^2,x,1) | 2·x−1 |
How to graph circles on a TI-89
A circle is not a function, because each x has two y values. The Y= editor only accepts y = something, so there are three ways around it.
1. Two functions
Solve x² + y² = r² for y and graph both halves. For a circle with radius 3 at the origin, type y1 = √(9 − x^2) for the upper half and y2 = −√(9 − x^2) for the lower half. The square root is 2nd ×.
For a circle with center (h, k), shift both halves: y1 = k + √(r^2 − (x − h)^2) and y2 = k − √(r^2 − (x − h)^2). Near the left and right ends the curve may show small gaps, because the halves are very steep there.
2. Parametric mode
Press MODE and set Graph to PARAMETRIC. The Y= editor now asks for pairs xt1 and yt1. Type xt1 = 3·cos(t) and yt1 = 3·sin(t), and set tmin to 0 and tmax to 2π in the WINDOW. The circle is drawn as one closed curve.
3. Polar mode
Set Graph to POLAR in MODE and type r1 = 3. A constant radius is a circle around the origin, and polar mode is also the place for spirals and rose curves.
Whichever way you choose, a circle only looks round when one unit on the x axis is as long as one unit on the y axis. On the handheld, open F2 Zoom on the graph screen and choose ZoomSqr after graphing.
Graphing inequalities
The TI-89 Titanium shades inequalities through the line style of a function. Type the boundary in the Y= editor, for example y1 = x² − 4 for y > x² − 4. With the cursor on y1, press 2nd F1 to open F6 Style and choose Above to shade the region above the curve, or Below for the region under it. Graph two functions with different styles and the overlap of the two shadings is the solution of the system.
Whether the boundary itself belongs to the solution is not shown by the shading, so decide that from the inequality sign: < and > exclude it, ≤ and ≥ include it. If you need the solution in x as an interval, use solve( on the home line with the inequality, for example solve(x^2 − 4 < 0, x), and read the bounds from the result. The < sign is 2nd 0 and > is 2nd ., ≤ and ≥ are ◆ 0 and ◆ .
In Calc89
Calc89 graphs functions, parametric curves, polar curves and sequences, so all three circle methods above work, and the CAS commands for zeros, extrema, intersections and tangent lines run on the home line with the same names. On the graph screen you get trace, zoom and a table, and the exact value is shown next to the decimal. The camera problem scanner puts a function from your worksheet straight into Y=, and the AI keystroke tutor shows the keys for a graphing question as tappable chips. Calc89 is free to download, with Pro features as an in-app purchase.
On exams, as of October 2026: phone and tablet apps are not permitted on standardized exams. The SAT (since August 2025) and the ACT prohibit CAS calculators, including the TI-89 Titanium. The AP Calculus and AP Physics exams permit the physical TI-89 Titanium.
Frequently asked questions
Why does my circle look like an oval on the TI-89?
The screen is wider than it is tall, so equal units on both axes need a square window. On the handheld use F2 Zoom, then ZoomSqr.
Why is there a gap at the left and right of my circle?
The two square root functions are very steep near the ends, and the plotted points miss the exact ends. Graph the circle in parametric or polar mode for a closed curve.
How do I get a table of values instead of a graph?
Press ◆ F5 for TABLE. ◆ F4 opens TBLSET, where you set the start value and the step.
Related pages
- /commands/zeros/
- /commands/fmin/
- /commands/fmax/
- /commands/tangentline/
- /commands/solve/
- /guides/ti-89-keystrokes-basics/
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