Graphing Calculator

How to use the graphing calculator

1. Type a function of x in the f₁(x) = field, for example sin(x) or x^2/4 - 2. The graph updates while you type.
2. Add up to four more functions in the other fields. Each one gets its own colour, shown by the dot in front of the field. Leave a field empty to hide it; Clear empties them all.
3. Move around the graph: drag it with the mouse or a finger, zoom with the mouse wheel or a two-finger pinch, or use the + and − buttons. Reset view brings back the default window, x from −10 to 10 centred on the origin.
4. Hover over the graph (or tap it on a touch screen) to trace: a dashed vertical line marks the x position and the value of every function at that x appears under the graph.
5. Click Download PNG to save the current view as an image, grid and axes included, ready for a worksheet, a report or a presentation.

If an expression cannot be read, a message under the field explains why and gives the position of the problem; the other curves keep working.

What you can type

• Variable: x. You may start with y = or f(x) =; it is ignored.
• Operations: + − * / and ^ for powers (also ² and ³). Powers are evaluated right to left, so 2^3^2 = 2^9, and −x^2 means −(x²), as in textbooks.
• Implicit multiplication: 2x, 3sin(x), 2pi, (x+1)(x−1) and x(x+1) are all products.
• Functions: sin, cos, tan, sec, csc, cot, asin, acos, atan, sinh, cosh, tanh, sqrt (or √), cbrt, abs (or |x|), ln (natural log), log (base 10), exp, floor, ceil, round and sign.
• Constants: pi (or π), e and tau.

Trigonometric functions work in radians, the standard for graphing. Functions accept brackets, sin(x), or the product that follows them: sin 2x is read as sin(2x), while sin x cos x is sin(x) × cos(x). You can also write sin^2(x) for (sin x)².

A negative number raised to a fraction with an odd denominator gives the real root, so x^(1/3) is drawn for negative x as well, just like cbrt(x).

Asymptotes and discontinuities

A naive plotter joins every sampled point with a straight line, which draws false vertical lines through the asymptotes of tan(x) or 1/x. This tool samples each function twice per screen pixel, then zooms in on every large jump between two neighbouring samples by repeated bisection. If the jump shrinks as the interval narrows, the function is simply steep and the points stay connected. If it does not — a vertical asymptote, a step of floor(x), or a point where the function is undefined — the curve is cut there and each branch is extended right up to the break.

The same bisection finds where a function stops being defined, so sqrt(x) starts exactly at x = 0 and ln(x) plunges towards the y-axis instead of ending one pixel early.

Tips

• Both axes use the same scale, so circles look round and a slope of 1 is a 45° line.
• To find an intersection or a root, zoom in on it with the wheel: the trace readout gives more digits as the scale grows.
• To compare a function with a transformation, type f₁ = x^2 and f₂ = (x − 3)^2 + 1, for example.