Function grapher
Type one or more functions: curves plot instantly, with the derivative, tangent, integral and key points. Drag to move the view, scroll or pinch to zoom.
Axes and grid
For an exact size on paper, print at 100% (no “fit to page”); the SVG and TikZ keep this scale too, and the PNG is saved at 300 dpi.
Table of values
How do I type a function?
- Operations:
+ - * / ^; multiplication can be implied:2x,3sin(x),(x+1)(x-1). - Functions:
sqrt,abs,exp,ln,log(base 10),sin cos tan(radians),asin acos atan,sinh cosh tanh,floor ceil sign. Constantspi(or π) ande. - Any other letter (a, b, k…) is a parameter, adjustable with a slider.
How is it computed?
The derivative is exact (differentiation rules, then simplification) and shown in maths notation. Zeros, extrema and intersections are found from sign changes of f, f′ or f − g, then refined by bisection. The integral uses Simpson's rule with 2,000 intervals.
Interpolation
Enter points (or take them from a plotted function) and pick a method: Lagrange or Newton polynomial (the same polynomial written differently, with the divided-difference table), Hermite polynomial that also matches given slopes, piecewise cubic Hermite, natural cubic spline or linear interpolation. Taking 11 equally spaced points of 1/(1 + x²) between −5 and 5 shows Runge's phenomenon; with Chebyshev nodes or a spline, the gap drops.
Frequently asked questions
How do I put the graph in a LaTeX document?
The “TikZ (pgfplots)” button gives code to paste into your document (trig functions are converted to degrees for pgfplots). See also the LaTeX assistant and TikZ to SVG.
Are my graphs saved?
They stay in your browser, and the share link holds the functions and the visible window.
Example: a full function study
Type x^2 - 2x - 3. The tool plots the parabola and gives:
- the zeros: x = −1 and x = 3 (the polynomial factors as (x + 1)(x − 3));
- the minimum: at x = 1, where f(1) = −4;
- the exact derivative: f′(x) = 2x − 2, plotted alongside, which is indeed zero at 1;
- the tangent at x = 3: y = 4x − 12;
- the integral from −1 to 3: −32/3 ≈ −10.67, negative because the curve lies below the axis between the roots.
To check hand-worked exercises, compare each result; to prepare a lesson, export the figure as TikZ (pgfplots) or SVG.
Using parameters
Any letter other than x and e becomes a parameter with a slider. Type a*x^2 + b and vary a: the parabola widens, narrows or flips when a goes negative; b shifts it vertically. With a*sin(b*x) you can see amplitude and period (2π/b). It is a great way to let students form conjectures before the proof.
Interpolation: for university
- Lagrange and Newton give the same polynomial through n points; Newton's form updates more easily when a point is added.
- Runge's phenomenon: interpolate
1/(1+25x^2)on [−1, 1] with 11 equally spaced points: the polynomial oscillates wildly near the ends. Switch to Chebyshev nodes and the error collapses. A classic numerical-analysis demo. - Cubic splines: piecewise, smooth and free of spurious wiggles; the usual choice for smoothing measurements.
- Hermite: also imposes derivatives at the points, useful in mechanics or animation.
Printing to scale
For an exact paper document (1 unit = 1 cm), turn on “fixed units” and print at 100%, without fit-to-page. SVG and TikZ keep the same scale; PNG is saved at 300 dpi. The table of values starts from the step you choose, ready for an exercise.
Common input mistakes
sin xmust be writtensin(x); angles are in radians.e^-xmust be writtene^(-x)so the sign applies to the exponent.logis base 10; the natural logarithm isln.
Guide written and checked by Erwan Hautot · updated 3 November 2026.