Disclaimer
Grafolyn is an educational tool. It is built carefully and tested thoroughly, but every numerical method has limits, and it is better to understand them than to discover them.
Educational use
The calculator and guides are intended to help people learn and check mathematics. They are not a substitute for instruction from a qualified teacher, nor for professional advice in engineering, finance, medicine, or any other field where a wrong number has consequences.
If you are using results here for anything where accuracy matters materially, verify them independently.
Numerical precision, and where it ends
The calculator uses double-precision floating-point arithmetic, the same standard as most scientific software. This gives roughly 15 to 17 significant decimal digits. Four consequences follow, and they apply to any tool built this way.
Rounding accumulates
Values that cannot be represented exactly in binary, such as 0.1, are stored as the nearest representable number. Repeated operations accumulate these tiny errors. It is why a root that should be exactly zero may be reported as 3 × 10⁻¹⁷.
Catastrophic cancellation
Subtracting two nearly equal numbers destroys precision. If both are accurate to fifteen digits and agree in the first twelve, the difference has only three meaningful digits left. This is the dominant error source in numerical work, and no amount of care in the code removes it.
Zoom has a floor
Past roughly 10⁻⁹ units per pixel, adjacent pixels no longer have distinct coordinates and the plot becomes noise rather than detail. The calculator stops zooming before that point. If you need finer resolution, shift the window so the region of interest is near the origin, where floating-point numbers are denser.
Sampling can miss features
The graph is drawn by evaluating the function at many points and refining
where the curve bends. This is adaptive rather than uniform, which catches
far more than a naive plot, but it is not a proof. A function with a feature
narrower than the refinement can reach may not show it. Extremely rapid
oscillation, such as sin(1/x) near the origin, cannot be drawn
faithfully by any pixel-based tool.
Specific things to be aware of
- Holes are invisible. A removable discontinuity is a single missing point, smaller than a pixel. It will not appear. Always check for cancelling factors algebraically.
- Points of interest are found within the visible window. Roots outside the current view are not reported. Zoom out before concluding there are none.
- Regression reports the fit you asked for. A high R² confirms the chosen model describes the data, not that the model is appropriate. It never implies causation.
- Implicit curves are contoured on a grid. Very fine features may be missed, and self-intersections may be approximated.
Content accuracy
The guides are written and reviewed carefully, but errors are possible. Where a source is cited, check it. Where a keystroke sequence is given for a physical calculator, note that these vary between operating system versions and models; the manufacturer's own guidebook is authoritative.
If you find an error, please report it. We correct mathematical errors as a priority and note the correction on the page.
Examinations
Information about which calculators are permitted in examinations is provided for general guidance and reflects published policy at the time of writing. Policies change. The examination board's current published rules are the only authority, and it is your responsibility to check them before test day.
No web-based calculator, including this one, is permitted during a standardised test.
External links and advertising
Links to other sites are provided for convenience. We do not control them and are not responsible for their content or accuracy. Advertisements are selected by third-party networks, not by us, and their appearance is not an endorsement.
Affiliation
Grafolyn is independent. It is not affiliated with, endorsed by, or connected to Texas Instruments Incorporated, Desmos Studio PBC, the College Board, ACT Inc., or any calculator manufacturer or examination board. All trademarks are the property of their respective owners.
No warranty
All material and functionality on this site is provided without warranty of any kind. See the terms and conditions for the full statement.