Function Graph Plotter

What does the function graph plotter do?

You type one or more expressions f(x) and the tool draws the curves on the same axes. It finds the roots in the visible range (where a curve crosses the x axis), the y intercept and the points where the curves cross each other, marks them on the graph and lists their coordinates in a table. Drag the graph with the mouse or a finger to pan, and use the wheel or two fingers to zoom.

How to type a function

Write the expression in the variable x: x^2 - 4, sin(x), 2x + 1, 1/x, sqrt(4 - x^2), e^(-x^2), ln(x), abs(x). The multiplication sign can be omitted, so 2x and 3sin(x) are valid. Trigonometric functions take radians. Type pi for π. The decimal separator can be a point or a comma.

Example

Enter x^2 and x + 2. The parabola and the line cross at two points. By hand: x² = x + 2 becomes x² - x - 2 = 0, which factors into (x - 2)(x + 1) = 0. The intersection points are (-1, 1) and (2, 4), and the table shows the same points.

Discontinuities

For functions such as tan(x) or 1/x the curve runs off to infinity at a pole. The tool examines the jump between neighbouring points and breaks the line where the curve is not continuous. That way no misleading vertical line is drawn through the pole. Functions such as the square root and the logarithm are simply not drawn where they are undefined.

Limits

Roots and intersections are searched only in the visible x range. The range is scanned in 2000 steps and wherever the sign changes the root is refined by bisection to about 12 digits. Two roots closer together than one scan step can be missed, so zoom in and look again when in doubt. Results are numeric and are not given in exact form with radicals or fractions. Implicit equations (such as x² + y² = 1), parametric and polar curves are not supported.