Function graphs — parameter sliders, intersection points and function analysis
Functions
Letters in a formula are parameters: y = kx + b gets sliders for k and b. Tap a number to type a value or the bounds; press ▶ to watch the graph change.
Graph
Mouse wheel — zoom, drag — pan. On a phone: pinch and swipe. Tap the graph to see the coordinates of a point.
Points on the graphs
Function analysis
Table of values
Edit X to calculate Y, or edit Y to solve X. You can add or remove columns.
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∫ Definite integral — the area under the graph
The integral of the selected function from a to b is the area between its graph and the x-axis (parts below the axis count with a minus sign). The region is shaded right on the graph.
The f′ button next to a formula plots its derivative — the “rate of change” graph. Where f′ is above zero, the original function grows; where below — it falls; where f′ crosses the axis, the function has a peak or a valley.
📚 Theory: what a function graph is
The graph of a function y = f(x) is all points of the plane with coordinates (x, f(x)). For example, for y = x² at x = 2 we get y = 4 — the point (2, 4) lies on the parabola.
It helps to know graphs by sight: y = kx + b — a line, y = x² — a parabola, y = 1/x — a hyperbola, y = sin(x) — a wave, y = √x — half of a parabola lying on its side.
The points where the graph crosses the x-axis are the roots of the equation f(x) = 0. Plot x^2 - 5x + 6 — the parabola crosses the axis at 2 and 3, and the list of points under the graph shows them exactly.
You can write: + − * / ^, parentheses, sin cos tan sqrt abs ln log exp, the numbers pi and e. Multiplication can be omitted: 2x, 3sin(x).
Solving an equation graphically means plotting both sides and finding the intersection points: for x² = x + 2 plot y = x^2 and y = x + 2; the x-coordinates of the intersections, x = −1 and x = 2, are the roots. A letter in a formula becomes a slider: with y = a and y = x^2 - 2x you can see for which a the equation has two roots, one or none.
Is it free to use?
Yes, this tool is free and needs no sign-up. Your file is processed right in your browser and is not uploaded to a server. There are no watermarks.