Function Graphing Calculator
Plot up to three functions on shared axes with automatic scaling, and find the roots, turning points, intersections and asymptotes visible in the window.
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A graph answers questions a formula does not
Whether a function has a root, how many, where it turns, whether it is bounded and how it behaves at the edges of a range are all immediate from a plot and can be laborious to derive. This is why plotting is the first step in almost any numerical work: it tells you where to look before any algorithm is pointed at the problem, and it catches the case where the function does not do what you assumed at all.
Sampling can lie
A plot is built by evaluating the function at a finite set of points and joining them. A function oscillating faster than the sample spacing produces a plot that looks smooth and is completely wrong, which is aliasing, the same effect that makes wagon wheels appear to spin backwards on film. Increasing the resolution and seeing whether the shape changes is the standard check, and a plot whose appearance depends on the sample count should not be trusted.
Discontinuities need care
A function with a pole, such as one over x, takes enormous values either side of it. Joining those samples with a line draws a near vertical stroke that looks like part of the curve and is not there at all. This tool breaks the line where consecutive samples jump implausibly far, so a pole appears as a genuine gap rather than as a spurious near vertical segment.
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Frequently Asked Questions
Why does my plot look wrong?
Most often aliasing: the function oscillates faster than the sample spacing, so the drawn shape is an artefact rather than the function. Increase the resolution and see whether the picture changes; if it does, the original was not to be trusted.
How are asymptotes handled?
The line is broken wherever consecutive samples jump by an implausible amount, so a pole appears as a gap rather than as a spurious near vertical stroke joining a huge positive value to a huge negative one.
How are roots and turning points found?
Roots by scanning for sign changes and refining each bracket by bisection. Turning points by looking for changes in the sign of the numerical derivative. Both are limited to what falls inside the plotted window and at the resolution used.
Can I plot several functions together?
Yes, up to three on shared axes, with their intersections found automatically. Comparing functions on the same axes is usually more informative than looking at them separately, particularly when you care about where one overtakes another.
What can I write in the function?
Arithmetic with the usual operators, powers with a caret, and the common functions: sin, cos, tan, their inverses, exp, ln, log, sqrt, abs and the hyperbolic ones. The constants pi and e are recognised, and implied multiplication such as 2x works.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter one or more functions of x and set the range to plot and analyse them.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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