TI-84 error · ERR: BOUND
ERR: BOUND on TI-84 — Fixing Bounds, Limits and Guesses
ERR: BOUND is one of the few TI-84 messages that reports a mistake in the setup rather than in the mathematics. The calculator was asked to search for an answer inside an interval, and the interval as defined cannot be searched — most often because its two ends are the wrong way round.
The routine that raises it is usually one of the numeric tools: finding a zero, an intersection, a maximum or a minimum, a derivative at a point, a definite integral, or a solution from the equation solver. All of them work by sampling a range of x-values, so all of them need a range that makes sense.
Because the message names a bound rather than a value, students often suspect a fault in their equation. Usually the equation is fine and the cursor was simply left on the wrong side when the bounds were marked.
What ERR: BOUND actually reports
The reference guide gives the message two causes, and both are about ordering. In a CALC operation or with the trace selection, you marked a left bound that is larger than the right bound. In fMin(, fMax(, solve( or the interactive equation solver, you entered a lower limit that is larger than the upper limit.
ERR: BOUND
1:Quit
2:Goto
After pressing ENTER
Choosing 2:Goto returns you to the command that started the search. Since the offending numbers were typed at a prompt rather than written on the line, the cursor has nothing useful to land on — re-running the routine with better values is faster than reading the line again.
The order rule, and why it is easy to break
The calculator marks bounds from left to right on the x-axis. If you press ENTER to set the left bound while the cursor sits to the right of where you will later mark the right bound, the interval runs backwards and the message appears.
Add a guess to the mixture and the problem compounds: the guess must sit between the two bounds as well, otherwise the error changes to ERR: BAD GUESS. The safe sequence is to position the cursor at the left-hand edge of the region of interest, mark it, move right, and mark again.
Y1=X²−4
The window makes this easier or harder. In a wide window a small nudge of the arrow key moves a long way along the axis, so it is easy to overshoot and mark the bounds in the wrong order. Setting the window so that the region of interest fills the screen is worth doing first; our notes on finding roots and intercepts cover the same step from the graphing side.
Errors that look like BOUND but are not
A search can fail for several different reasons, and the calculator names most of them separately. Knowing which message belongs to which failure saves a lot of trial and error.
| What went wrong | Message you see | What to change |
|---|---|---|
| Bounds marked right to left | ERR: BOUND | Mark the left bound at the smaller x-value |
| Lower limit larger than the upper limit | ERR: BOUND | Swap the two limits in fMin(, fMax(, solve( or Solver |
| Interval contains no sign change | ERR: NO SIGN CHNG | Widen or move the interval |
| Guess outside the bounds, or surrounded by undefined points | ERR: BAD GUESS | Place the guess inside the bounds and near the answer |
| The interval straddles a point where the function is not defined | ERR: SINGULARITY | Move the interval clear of the singularity |
| The routine reached its iteration limit | ERR: ITERATIONS | Change the bounds, the guess, or both |
| The requested tolerance cannot be achieved | ERR: TOL NOT MET | Relax the tolerance or reformulate the equation |
| Window variables cannot be drawn | ERR: WINDOW RANGE | Correct Xmin, Xmax and the scales |
When the integral reaches outside the function’s domain
A definite integral computed with fnInt( is sampled across the interval, and the algorithm needs a real value at every point it visits. If the integrand is undefined somewhere inside the limits — ln(x) across an interval that includes zero, or a square root across negative x-values — there are no usable samples in that stretch and the calculation cannot complete.
TI does not give this case its own entry in the error table, and in practice the message may be ERR: DOMAIN rather than ERR: BOUND, because the argument has left the range the function accepts. Either way the diagnosis is the same: check the function over the whole interval before trusting the limits. Splitting the integral into two pieces that avoid the problem point, or moving the limits to the defined region, is the reliable repair. The definite integrals walkthrough sets out the keystrokes and the checks worth making first.
What to do when the interval is genuinely correct
If the bounds are in the right order and the message still appears, the interval itself is the problem rather than its order.
- Widen it. A root that lies just outside the marked section produces no sign change, and widening by a few units usually captures it.
- Move it. If the visible window shows one crossing but the equation has two, you may be searching the wrong region. Graph the equation first and look at where the curve actually crosses the axis.
- Supply a guess. Routines that accept one use it to choose a starting point; a guess near the expected answer shortens the search and avoids the parts of the graph that are undefined.
- Rephrase the equation. A solver works on the difference between two sides, so rewriting
3/(x−2) = xas3/(x−2) − x = 0is often easier for the algorithm than the original form. The equation solving walkthrough describes the solver’s prompts in order.
On the calculator the same principle appears in the table feature, where a ΔTbl of zero cannot step and a very large TblStart produces successive values beyond the range the calculator can represent. Those set-ups are reported as ERR: INCREMENT or ERR: OVERFLOW rather than ERR: BOUND, but the underlying lesson is the same: every numeric routine needs an interval it can actually walk through.
Worked example: a reversed interval at the zero prompt
Suppose Y1 is X²−4 and you want the positive root. You choose CALC ▸ 2:zero. The calculator asks for a Left Bound. In a wide window it is easy to press ENTER while the cursor is still at x = 3, then move left and press ENTER again at x = −1.
ERR: BOUND
1:Quit
2:Goto
Left bound marked at x = 3, right bound at x = −1
Quitting the message and running 2:zero again, this time marking the left bound at −1 and the right bound at 3, produces the root. The keystrokes are identical apart from the order in which the two ends are marked, which is why reading the prompt text before pressing ENTER is the habit that prevents this error.
Keeping the message away on exam day
Numeric tools are used heavily on the AP Calculus and IB papers that permit a graphing calculator, and a refused search mid-question costs time that is hard to recover. Setting a sensible window before using any CALC option, and marking the left bound before the right every time, removes almost every instance of this error. Exam rules are occasionally revised, so check the current wording with your board and your teacher. If the fault turns out not to be the interval at all, the full list of TI-84 error codes will point you to the message that fits.
Frequently asked questions
What does ERR: BOUND mean in plain English?
A numeric routine that works by searching an interval was given an interval it cannot use. Usually the two ends are the wrong way round: the left bound is larger than the right bound, or the lower limit is larger than the upper one. Swapping them clears the message.
Why does the calculator need a left bound and a right bound at all?
Routines such as zero, intersect and minimum cannot search an infinite graph, so they ask you to mark the section of the x-axis to inspect. The bounds are a search range, not part of the mathematics, which is why a wrong interval can be corrected without changing the equation.
Is ERR: BOUND the same as ERR: NO SIGN CHNG?
They are neighbours rather than synonyms. BOUND means the interval was defined impossibly, for instance with the bounds reversed. NO SIGN CHNG means the interval was reasonable but the function has no root inside it, so the search had nothing to close in on.
What should I do when the integral limits reach outside the function's domain?
Sketch the integrand first, because a numeric integral needs a value at every point it samples and an undefined region stops the calculation. You may see ERR: DOMAIN rather than ERR: BOUND in that case. Move the limits to a region where the function is defined, or split the integral around the problem point.
Can I avoid these messages by setting the window differently?
Often, yes. A wide window makes it easy to place the cursor outside the part of the curve you care about, which is how reversed bounds happen. Setting a window that frames the region of interest keeps the cursor, the bounds and the guess inside sensible values.
Official references
Statements on this page are checked against the manufacturer or exam authority documentation below. Where an official source and this page disagree, the official source wins.