How to use the graphing calculator
- Type a function of x into the f1(x) box, for example x^2 - 2 or 2sin(x). Press Add a function for up to six curves. Each curve has its own color and line style, so they can be told apart without color.
- Move the window by dragging the graph, with the arrow keys when the graph is selected, or by typing x min, x max, y min and y max. Zoom in, Zoom out, Equal scales and Reset window are one press away. Hold Ctrl and scroll to zoom at the pointer.
- Under the graph, read the zeros of each function in the current window, the point where two functions meet, and the value at x = 0. The table of values starts at any x and uses any step.
- Choose Radians or Degrees for the trigonometric functions. Use Copy results to copy the zeros, meeting points and table, or Download PNG to save the picture.
A parabola and a sine curve
With the starting functions x^2 - 2 and sin(x) in the window from -8 to 8, f1 has zeros at x = -1.41421 and 1.41421, the two square roots of 2 with their signs. f2 has zeros at -6.28319, -3.14159, 0, 3.14159 and 6.28319. The two curves meet at (-1.06155, -0.873112) and at (1.72847, 0.987596).
The table of values starting at -3 with a step of 1 shows f1 as 7, 2, -1, -2, -1, 2, 7 for x from -3 to 3, which matches the shape of the parabola with its lowest point at x = 0, where f1 is -2.
What you can type
Write expressions the way you would on paper. Use ^ for powers (x^2, 2^x), * or a space or nothing for multiplication (2x, 3(x+1), x sin(x)), and / for division. A leading "y =" is accepted. Multiplication written without a sign has the same rank as a written * so 1/2x means (1/2) times x, and a power binds tighter than a minus sign, so -x^2 is the negative of x squared.
The reader knows these functions: sin, cos, tan, cot, sec, csc, asin, acos, atan, atan2, sinh, cosh, tanh, asinh, acosh, atanh, sqrt, cbrt, abs, exp, ln, log (base 10, or log(x, base) with two values), log2, floor, ceil, round, trunc, sign, fract, min, max, pow, mod and hypot, and the constants pi, e and tau. Functions need parentheses around their values, as in sin(x).
Asymptotes, steps and gaps
Where a function has no value, such as sqrt(x) for negative x, nothing is drawn. Where it shoots off to plus and minus infinity, as tan(x) and 1/x do, the line is broken so no false vertical line joins the two sides. Steps such as floor(x) are drawn as separate flat pieces.
A jump is believed only when it stays as large when the interval around it is cut in half again and again. That keeps steep but continuous curves such as exp(x) or x^9 in one piece. Very large values are clamped for drawing and never turn into infinity on the canvas.
How zeros and meeting points are found
Each function is sampled at 4,000 points across the window. Where the sign changes between two samples, the zero is narrowed down by repeated halving, and a place where the curve shoots to infinity is rejected so a pole is not reported as a zero. Curves that only touch the axis, such as x^2 or abs(x), are found by a search for the lowest value of the absolute height.
Meeting points are the zeros of the difference between two functions. The method was checked against known answers: the square roots of 2, the multiples of pi for sine, the crossings of x^2 and x + 2 at -1 and 2, and sine against cosine at pi/4 and 5pi/4. For related tools see the quadratic equation solver and the scientific calculator.
Assumptions and limits
- Only functions of x are plotted. Equations such as x^2 + y^2 = 1, vertical lines such as x = 3, parametric curves and inequalities are not supported.
- Zeros and meeting points are searched only inside the current window. Two zeros closer together than one 4,000th of the window may be missed, and a very narrow spike that never lands on a sample can be missed in the picture as well.
- Expressions are limited to 300 characters. The window can be anywhere from 0.000000001 to 1,000,000,000 units wide or tall.
- Values are computed with ordinary double precision numbers, so results are shown to six significant digits and tiny rounding noise near zero is possible.
Frequently asked questions
Is the expression I type run as code?
No. The text is read by a small reader that builds a tree out of numbers, x, operators and a fixed list of functions. It never calls eval or builds new functions from text, and names such as constructor or window are simply rejected.
Why does the graph have a gap?
A gap means the function has no real value there, or that it jumps across the window like tan(x) at an asymptote or floor(x) at a step. Zoom in on the gap to check, or use the table of values for exact numbers around it.
How do I plot the cube root of a negative number?
Use cbrt(x). A power such as x^(1/3) has no real value for negative x on a calculator that works with real numbers, so it is left out of the graph there.
Can I get the graph without using a mouse?
Yes. Tab to the graph, then use the arrow keys to move the window, plus and minus to zoom and 0 to reset. The table of values and the lists of zeros give the same information as text.