Graph Results
Enter an expression, then select Plot Graph.
Interactive Graph
Formula Used
Derivative: f′(x) ≈ [f(x + h) − f(x − h)] ÷ 2h
Definite integral: ∫f(x)dx using Simpson’s numerical rule
Polar conversion: x = r cos(θ), y = r sin(θ)
Parametric curve: x = x(t), y = y(t)
The calculator samples each expression across the selected viewing range. It evaluates values with Math.js and draws curves with Plotly. Numerical methods estimate roots, derivatives, integrals, and important graph points.
How to Use
- Add a function, dataset, inequality, or specialised curve.
- Enter expressions using standard mathematical notation.
- Choose ranges, precision, line style, and display options.
- Select Plot Graph to create the interactive visualisation.
- Use analysis tools for roots, slopes, areas, or intersections.
- Build tables and export results in several useful formats.
Use an asterisk for multiplication when an expression is unclear. Enter powers with the caret symbol, such as x^2. Complex functions may require smaller ranges or more sample points.
Example Data
| Graph type | First expression | Second expression | Purpose |
|---|---|---|---|
| Function | x^2 - 4*x + 3 | — | Plot a quadratic curve. |
| Parametric | cos(t) | sin(t) | Draw a unit circle. |
| Polar | 2*sin(3*theta) | — | Draw a three-petal rose. |
| Implicit | x^2 + y^2 = 25 | — | Draw a radius-five circle. |
| Scatter | -2,-1,0,1,2 | 4,1,0,1,4 | Plot paired data points. |
Frequently Asked Questions
Which expressions are supported?
Standard arithmetic, powers, roots, logarithms, trigonometry, and constants are supported. Math.js also supports absolute value, floors, ceilings, and many functions. Use explicit multiplication when the parser reports an unclear expression.
Can I graph several equations together?
Yes, add multiple expression rows and keep them visible. Each row can use a different colour, line width, and style. Hidden rows remain saved but do not appear.
How are roots calculated?
The calculator scans the selected interval for sign changes. It then refines each detected root with bisection. Tangential roots may require a narrower range or direct inspection.
Are derivative and integral results exact?
No, those results use numerical approximations. Accuracy depends on scale, smoothness, and selected bounds. Increase sampling cautiously when curves change very quickly.
How do degree and radian modes differ?
Radian mode uses standard mathematical angle values. Degree mode converts trigonometric inputs before evaluation. Polar parameter limits still use the displayed angle mode.
Can I graph inequalities?
Yes, enter forms such as y >= x^2 - 4. The calculator shades values satisfying the relationship. Complex compound inequalities are not supported.
Can I save my graph?
Use Save Settings to store the current setup locally. Load Settings restores expressions, ranges, and display choices. Browser storage must remain enabled for this feature.
Why does a curve show gaps?
Gaps usually indicate undefined values or vertical asymptotes. They prevent misleading lines across discontinuities. Enable Connect Gaps only when the connection is mathematically appropriate.
Which export formats are available?
You can export CSV tables, PNG images, SVG images, and PDF reports. Copy Results copies the current analysis text. Printing creates a clean page containing results and graphs.