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Graphing Calculator

Type a function of x and choose the range of x to draw.

Use x, + − * / ^, brackets, sin, cos, tan (radians), ln, log, sqrt, pi and e. Example: x^3 − 4x or sin(x)/x.

Colour 1

Optional. Add a second function to compare, for example a line that crosses the curve.

Colour 2

Leave y min and y max blank to fit the graph automatically.

Spacing between grid lines, in units of x and y.

Resolution

Higher draws a smoother curve but takes longer.

Show grid
Show axes
Show labels
Equal aspect ratio

Makes one unit on x as long as one unit on y, so circles look round and angles are true.

Show coordinates on hover
Advanced
Colour 3
Colour 4

This result is an estimate only. Double-check important figures before relying on them.

How it is calculated

  • f(x) is calculated at 201, 501 or 1,501 evenly spaced points (low, medium, high resolution) from the start to the end of the range
  • Points where f is undefined leave a gap in the line
  • Each sign change is refined by bisection to find the zero crossing

For exact roots of a polynomial, use the polynomial roots calculator.

Worked example

y = x² − 2x − 3 from x = −5 to 5:

  • Crosses zero at x = −1 and x = 3
  • Lowest point −4 (at x = 1), highest 32

Why your number may differ

Very steep or fast-wiggling functions can hide detail between sample points. Zoom in by narrowing the range. Roots that only touch zero without crossing may not be found.

Frequently asked questions

Which functions can I plot?

Polynomials, fractions, powers, roots, logarithms and trigonometric functions of x. Trigonometric functions use radians.

How are zero crossings found?

The graph is sampled at 500 points (medium resolution), and every change of sign is narrowed down to 6 decimal places. A jump across an asymptote, like 1/x at 0, is not counted.

Can I plot several functions together?

Yes. Fill in up to four functions, each with its own colour. The analysis lists the intercepts, lowest and highest values for each one.

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