Function graphs — type a formula and move the plot around like a map
Functions
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.
Mouse wheel — zoom, drag — pan. On a phone: pinch and swipe.
Table of values
Edit X to calculate Y, or edit Y to solve X. You can add or remove columns.
| X |
|---|
| Y |
∫ Definite integral — the area under the graph
The integral of the first 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.
📚 Theory: what a function graph is
The graph of 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 sideways parabola.
The points where the graph crosses the X axis are the roots of f(x) = 0. Plot x^2 - 5x + 6 and you will see the parabola cross the axis at 2 and 3 — the same roots the equation solver finds.
You can write: + − * / ^, parentheses, sin cos tan sqrt abs ln log exp, the numbers pi and e. Multiplication can be omitted: 2x, 3sin(x).