1. Understand the shared workspace
The four dedicated pages open Functions, Shading, Table or Revolution automatically. They share one workspace; a saved project preserves the editable Functions, Table, Shading, Revolution and Axes scopes.
- Use the left tabs for Functions, Table, Shading, Revolution, Analysis, Points and Axes. Analysis or Points may be hidden by the administrator.
- Click a mathematical input field to open the symbol palette for fractions, roots, powers, trigonometric functions and relation symbols; normal keyboard input still works.
- The top toolbar contains zoom, reset, A, Insert image, Undo, Redo, Save, HTML, Open, PNG, SVG and Copy. Line/Arrow buttons appear in the modes that support them.
- Collapse the sidebar when more drawing space is needed, and use Reset view to return the graph viewport to its configured bounds.
2. Plot functions, curves and relations
Add as many objects as the site limit allows and choose the correct graph type before entering the expression.
- y = f(x): standard Cartesian functions with optional xmin and xmax.
- x = f(y): sideways functions with optional ymin and ymax.
- Parametric: enter x(t) and y(t); Polar: enter r(t). Set the parameter interval in From and To.
- Equation / Inequality: enter an implicit equation or inequality; the fill and boundary style follow the relation.
- Each object has visibility, color, thickness and line-style controls. Collapse a card to keep a long function list manageable.
3. Analyze functions and plot point data
Choose a valid function in Analysis. Exact inputs such as fractions, roots, π and e are accepted where supported.
- Calculate a function value, display f′, draw a tangent or normal line, and find zeros and extrema/stationary points.
- Set a and b to calculate an integral, area or arc length; enable Shade region when a visual area is useful.
- Enable Trace points with pointer to inspect coordinates interactively on the graph.
- In Points, enter one x,y pair per line, choose point color and size, connect the points, or fit a linear or quadratic trend line.
- Analysis results are mathematical assistance. Check the function, interval and assumptions before using a result in formal work.
- Analysis results and the Points data list are not included in .ogp project files. Save, record or export important data and calculated results separately.
4. Shade regions accurately
Create the boundary graphs in Functions before opening Shading.
- Between graphs with an x-bound: choose two y = f(x) functions and xmin–xmax.
- Between graphs with a y-bound: choose two x = f(y) functions and ymin–ymax.
- One-sided shading supports above/below y = f(x), left/right of x = c, above/below the x-axis and left/right of the y-axis.
- Choose color, opacity and a solid, stripe, crosshatch or grid pattern. Add multiple regions, then edit or delete them from the region list.
- Clear all affects the selected shading group without deleting the underlying functions.
5. Create variation and derivative-analysis tables
Select the function and either its real domain or a custom interval, then choose the table type.
- Variation Table uses x, f′(x) and f(x), derivative signs, variation arrows, extrema, infinities and discontinuity markers.
- First Derivative Sign Chart emphasizes intervals, sign of f′(x), function behavior and values.
- First and Second Derivative Analysis Table combines f′ and f″ signs with monotonicity, concavity and inflection points.
- The exact-analysis engine checks domain, limits, derivatives, roots, extrema and sign intervals, preserving fractions, roots, π and e when possible.
- Customize the outer frame and horizontal/vertical lines. Format object groups, or double-click one item to edit, drag, rotate or delete it.
- Use A, Insert image, Line and Arrow to add explanatory objects. Recalculate when you want to rebuild the table from the function.
6. Build a solid of revolution
Define two graph boundaries and an interval before opening Revolution.
- Select First graph, Second graph, a, b and the x-axis or y-axis. One boundary may be y = 0.
- Use Draw solid of revolution for the illustration or Calculate volume to calculate and display the volume result.
- Show or hide the middle cross-section, solid fill, between-graph fill, cross-section fill, both base diameters and axis labels.
- Choose separate colors for the solid, original region and cross-section. Add or edit construction lines and arrows directly on the figure.
- If the figure is empty, check that a < b and the two boundaries form a nonzero region over that interval.
7. Customize axes and editable objects
Axes and inserted objects are part of the saved project and exported graphic.
- In Axes, set x/y bounds, grid style, axis visibility and style, major ticks, tick length, number visibility, fonts and colors.
- Use Equal axis scale or set the length of one x-axis unit relative to one y-axis unit. Choose radians/degrees, legend and graph title.
- Drag axis numbers and O/x/y symbols. Double-click an axis, tick, number or symbol to open its editor; Delete/Backspace removes the selected object.
- A inserts either plain text or an Alpha Formula. Double-click later to edit content, font, size, color, position or rotation.
- Insert image reads a local image into the browser project. Drag it, resize with corner/side handles, rotate it and choose Front or Back; it is not uploaded by the theme.
- Line and Arrow objects can be moved, resized, rotated and formatted with color, thickness and solid/dashed/dotted styles.
8. Save and reopen the editable project
Use a project file when the drawing must remain editable rather than being flattened into an image.
- Save downloads an .ogp file containing functions, tables and table edits, shaded regions, solid settings, axes, text, formulas, images and object styles.
- Open validates and loads an .ogp file from the same or another device. Existing project state is replaced by the opened file.
- HTML creates a small launcher file. Opening it starts a real OnlineGraphing.com tab and transfers the project through the browser; the launcher also provides an .ogp backup path.
- Analysis results and Points-tab entries belong to the working session and are not restored from an .ogp project. Record or export important data separately.
- Keep the project file in a known folder and save again after important edits. PNG/SVG files cannot restore the editable workspace.
9. Export and copy the finished graphic
Choose the output according to where the graphic will be used.
- PNG is a raster image suitable for quick insertion into Word, presentations and learning platforms.
- SVG stores vector geometry and is the best choice when the graphic must remain sharp after enlargement or further editing.
- Copy places a rendered image on the clipboard for pasting into Word or image-editing software.
- Variation-table PNG, SVG and Copy use the same collision-safe layout, including edited values and inserted objects.
- Before export, check the viewport, object layers, font sizes, line styles and whether every intended annotation is visible.
10. Practical tips and common checks
Most unexpected results come from the selected graph type, interval or object state rather than the export command.
- Use exact notation such as 1/3, sqrt(2), root(2,3), pi/6 and e/2 when exact values matter.
- For shading and solids, verify that the selected boundary functions are compatible and distinct on the chosen interval.
- For a variation table, use Recalculate after changing the function or interval; manual table edits are intentionally preserved until rebuilt.
- A single click selects an object; double-click opens its editor. Dragging moves it, while Delete/Backspace removes the current selection when supported.
- Use Undo/Redo for recent changes and an .ogp file for a durable backup of the supported editable Functions, Table, Shading, Revolution and Axes scopes.