Function Graph Workbench
Explore a function over a chosen x and y window using a deliberately limited parser. The graph, undefined samples, residual-checked root candidates and two-step slope estimate stay in your browser. Sampling is exploratory and cannot prove continuity, every root, or an exact derivative.
Key features
- Parse only x, parameter a, constants pi/e, basic arithmetic, integer powers and seven named functions
- Plot 401 evenly spaced samples with explicit undefined, clipped and suspected-gap intervals
- Inspect f(x) at a probe and a centered finite-difference slope with stability indicators
- Report at most 12 sampled or sign-change root candidates with residual and bracket width
- Switch among quadratic, pole, square-root domain and parameter examples
- Download versioned project JSON, plotted SVG or sampled-value CSV
How to use
- Choose a preset or enter an explicit formula such as x^2-4, 1/(x-1), sqrt(x), or a*sin(x).
- Set parameter a, numeric x/y bounds and a probe x, then apply. Invalid edits leave the current graph intact.
- Read f(x), possible domain gaps, root candidates and the slope stability figures alongside the plot.
- Move the probe with its numeric field and apply again; use keyboard scrolling to inspect the wide SVG on a phone.
- Export JSON for later import, SVG for a visual reference or CSV for the 401 sampled values.
Use cases
- Compare a polynomial's sampled roots with its visible curve
- See how a reciprocal pole differs from a root
- Explore the real square-root domain within a selected window
- Change a parameter and compare a family of sine graphs
Frequently asked questions
Does a listed root mean an exact solution?
No. It is a sampled zero or a sign-change candidate accepted only when a numerical residual is at most 1e-7. Even-multiplicity roots between samples and narrow features can be missed; poles are rejected when the residual check fails.
Are gaps proofs of discontinuity or domain boundaries?
No. A gap may come from an undefined sample, clipping outside the chosen y window or a midpoint jump heuristic. The grid can miss narrow gaps, and a clipped curve may be continuous.
How accurate is the slope?
It is a centered finite difference at two step widths. The displayed difference between estimates and between left/right slopes is a stability indicator, not a rigorous error bound. Undefined, cusp-like or unstable probes show unavailable rather than a derivative.
Which formulas work?
Use explicit multiplication, x, a, pi, e, parentheses, + - * /, integer exponents from -8 to 8, and sin, cos, tan, sqrt, ln, abs or exp. Trigonometric input is in radians. Implicit multiplication, units, equations, other functions and arbitrary code are rejected.
Does the tool send my formula anywhere?
The workbench runs calculations in the tab and offers local downloads. It does not submit your formula to a calculation service or save it automatically.
Privacy
Formula and project JSON are processed in this browser tab. Downloads remain on your device. No remote calculation or automatic persistence is used.
Comments & questions