Graphing Calculator

Draw up to three real functions on the same Cartesian axes and download the labelled graph as a PNG. Choose the horizontal and vertical windows yourself, then evaluate each expression at a separate x value. This is useful for comparing shapes, exploring transformations and illustrating a calculation.

How to use this tool

1. Enter one function per line, using x and explicit multiplication such as 2*x.
2. Choose increasing minimum and maximum values for both axes. The two axes need not share the same scale.
3. Enter the x value for the numerical probe and select Calculate.
4. Inspect the picture and probe values. Narrow the window when a feature needs closer examination, or download the PNG.

Formula

y = f(x); graph coordinates are mapped linearly from the selected x/y window to the image.

The expression grammar supports +, -, *, /, ^, parentheses, x, pi and e. Available single-argument functions are sin, cos, tan, asin, acos, atan, sqrt, abs, ln, log, exp, floor and ceil. All trigonometric inputs and inverse-trigonometric outputs use radians. Powers associate right to left; unary minus has lower precedence than a power. Narrow windows may use explicitly labelled axis offsets. Limits and the probe must lie within ±1e12; ranges too close for floating-point sampling are rejected.

Example

For x^2 - 4, a probe at x = 3 gives 5. The parabola crosses the horizontal axis at x = -2 and x = 2; a window from -4 to 4 horizontally and -5 to 12 vertically shows both crossings and the vertex.