How to use it
- Type an expression in a row:
y = x^2 - 4, or justx^2 - 4. Each row gets its own color; the dot beside it hides or shows the curve. - Use any other letter as a parameter and give it its own row, such as
a = 2: a slider appears, and every curve usingaredraws as you drag it. If you type a letter with no row yet, a button offers to add one. - Drag the graph to move around, scroll or pinch to zoom, and tap a curve to read its coordinates.
x = 3draws a vertical line. - The table under the graph lists the roots, y-intercepts, maxima, minima and intersections in view; tap one to mark it. Copy link puts the expressions in a shareable link and Download PNG saves the picture.
What you can type
| To get | Type | Notes |
|---|---|---|
| Powers and roots | x^2, x², sqrt(x), cbrt(x), x^(1/3) | powers group from the right, so 2^3^2 is 2^9 = 512, and -x^2 means -(x^2) |
| Multiplication | 2x, 3sin(x), (x+1)(x-1), 2pi x | writing things side by side multiplies them; 1/2x is (1/2)x, so write 1/(2x) for the other reading |
| Trigonometry | sin cos tan sec csc cot asin acos atan sinh cosh tanh | angles in radians; sin x works without brackets, but sin 2x is sin(2)·x, so write sin(2x) |
| Logs and exponentials | ln(x), log(x) (base 10), log2(x), e^x, exp(x) | e and pi (or π) are the constants |
| Other | |x| or abs(x), floor, ceil, round, min(a,b), max(a,b), mod(x,3), x! | mod always returns a value between 0 and the divisor, so mod(-1,3) is 2 |
Odd roots of negative numbers are real, as on a school calculator: x^(1/3) at x = −8 is −2 and (-8)^(2/3) is 4, so the graph of x^(1/3) has a left half. Square roots and logarithms of negative numbers are left undrawn rather than shown as complex numbers.
Drawing curves honestly near asymptotes
A graphing calculator samples a function at a few thousand points and joins them with straight lines. The trap is joining two points on opposite sides of an asymptote: tan x just left of π/2 is huge and positive, just right of it huge and negative, and a naive plot draws a vertical line between them that is not part of the graph. This calculator only joins two samples that are far apart on screen if the function moves steadily from one to the other at eight points in between; across an asymptote it does not, so the line is broken there, while a steep but continuous curve such as x^9 stays in one piece.
The same idea keeps the points table honest. A root is a place where the curve crosses zero, found where neighboring samples change sign and then narrowed down by bisection to the limit of double-precision arithmetic; a sign change caused by a jump (floor x − 0.5) or an asymptote (1/x) is not a root and is not listed. Maxima and minima are refined by golden-section search, and a spike toward an asymptote, such as 1/x² at zero, is not reported as a maximum.
What we tested
On October 15, 2026 we ran the page’s own functions against Python’s math library and closed-form answers. 49 hand-picked expressions (implicit multiplication, power order, functions without brackets, superscripts, absolute-value bars, odd roots of negatives) gave the expected value, and 8 malformed ones gave an error message instead of a number. 2,000 randomly generated expressions evaluated at 9,491 points matched Python to within 2e-14 relative error. Roots of polynomials, sin x, tan x, e^x − 5 and ln x came out within 3e-15 of the exact values, with no false roots at the asymptotes of tan x, 1/x and 1/(x² − 1) or at the jumps of floor x; maxima and minima of x³ − 3x, cos x, x e^−x and x⁴ − 2x² matched calculus, and sin x and cos x crossed exactly at π/4 + kπ. Across −10 ≤ x ≤ 10, tan x and sec x were drawn as 7 separate pieces, broken at each asymptote. In Chromium: the default rows listed sin x's roots (3.141593 …) and its intersections with the parabola; for x³ − 3x and x + 2 the table showed the maximum (−1, 2), the minimum (1, −2) and the three intersections (x = −1.675131, −0.5391889, 2.21432, the real roots of x³ − 4x − 2); tapping the cubic near x = 2 showed (2, 2.000004) (a point on the curve at the tapped pixel); dragging and scrolling moved and zoomed the view; an unknown letter offered a slider button, and dragging the slider redrew the graph; an incomplete expression showed a message; a copied link reopened with the same four rows; the PNG downloaded; the page fitted a 390 px phone with no errors. We also checked the check: with the asymptote test switched off, tan x and sec x came out as a single unbroken line and the test failed.
Tips
- To solve an equation such as x³ = 2x + 1, graph both sides as two rows and read the intersections from the table.
- Zoom in on a point in the table to see more digits of it; the coordinates shown are rounded to 7 significant figures.
- Sliders run from −10 to 10 in steps of 0.1; type a value in the row (a = 25) to go beyond that.
- To compare a family of curves, use the same slider in several rows, for example y = a x^2 and y = a x^2 + 1.
Sources
Checked on .
Frequently Asked Questions
Built by Derek Giordano · Part of Ultimate Design Tools