Function Graph Plotter — Draw and Analyse Any Curve Online
A function graph plotter turns an algebraic expression into a picture. Type something like x^3 - 3x + 1, sin(x)/x or exp(-x^2), choose an x-window, and the curve appears with labelled axes, a grid and every interesting feature marked. Everything runs in your browser, so there is nothing to install and nothing you type leaves your device.
How the plotter builds a curve
Your expression is parsed once into a syntax tree and compiled, then evaluated at several hundred evenly spaced x values across the window. Compiling first and evaluating many times is what keeps the online graphing calculator fast enough to redraw while you type. Each evaluation is guarded, so a value that is undefined, infinite or complex becomes a gap rather than an error. That is why sqrt(x) simply stops at the origin, and why tan(x) is drawn as separate branches instead of one line crashing through each asymptote.
What the tool works out for you
The same samples that draw the curve also drive a full numerical analysis. Consecutive points that straddle zero bracket a root, which is then refined by bisection to a tolerance near 1e-10. Sign changes in the numerical derivative locate local maxima and minima, classified by the direction of the change. Applying the same routine to the difference between two curves finds their intersections — the graphical way to solve an equation such as x^2 = x + 2, whose crossings at (−1, 1) and (2, 4) are exactly the algebraic solutions.
You also get the y-intercept, the range attained across the window, detected discontinuities, and whether the function is even, odd or neither. Turn on Show derivative to overlay a dashed f'(x), or Show definite integral to shade the signed area between two bounds. The area is computed with composite Simpson's rule over a thousand subintervals, which is exact for cubics and extremely close for any smooth function.
Beyond y = f(x)
Many important curves cannot be written as a single function of x. Parametric mode sweeps a parameter t and plots the point (x(t), y(t)), which is how you draw circles, ellipses and self-intersecting Lissajous figures. Polar mode sweeps an angle and plots r(θ), converting to Cartesian coordinates with x = r·cos(θ) and y = r·sin(θ) — the route to cardioids and rose curves. Switch on the equal-aspect option in either mode so that a circle renders as a genuine circle rather than an ellipse.
Writing expressions the plotter understands
The parser accepts ordinary mathematical notation: + - * /, ^ for powers, brackets for grouping, and named functions including sqrt, abs, exp, log, log10, the trigonometric family, their inverses and the hyperbolics. Implicit multiplication is handled, so 2x, 3(x+1) and 2sin(x) all mean what you expect. The constants pi and e are built in — and the window boxes accept expressions too, so an x-range of -2*pi to 2*pi is entered directly rather than approximated as −6.28.
Three named parameters, a, b and c, can appear anywhere in an expression and are driven by sliders. Plot a*sin(b*x) and drag them to watch amplitude and frequency change in real time, or press play to sweep a automatically — an unusually direct way to see what a coefficient actually does to a family of curves.
sin(1/x) near the origin, or a root squeezed between two sample points can be missed entirely. If a curve looks suspicious, raise the sample count or zoom into the region before trusting what you see.Degrees, radians and reading the results
The angle unit changes how every trigonometric function interprets its argument. In radians sin(90) is about 0.894; in degrees it is exactly 1. The setting applies to inverse functions in reverse — asin(1) returns 90 in degrees and 1.5708 in radians — and to the polar sweep, where a full revolution is 0 to 360 or 0 to 2*pi respectively. Calculus results such as derivatives and integrals of trigonometric functions only take their familiar textbook forms in radians, so keep radians selected for coursework unless a question explicitly asks otherwise.
Hovering the plot traces the analysed curve, reporting the exact coordinate and the slope under the cursor. Drag to pan, scroll to zoom, and export the finished picture as PNG or SVG for a report or a worksheet, or the sampled points as CSV for a spreadsheet.