What the graphing calculator does
Each line you type is a function y = f(x). The calculator draws all of them on one grid, each in its own color, and redraws as you type. Below the graph it lists where each curve crosses the x-axis and where two curves meet, and the table of values gives exact numbers at the x values you choose. Everything is worked out in your browser.
It uses the same expression engine as the scientific calculator, so the order of operations is the same: powers before multiplication, multiplication before addition, and −x² means −(x²). A missing × counts like a written one, so 2x, 3sin(x) and (x + 1)(x − 2) all work.
What you can type
| Type | Meaning |
|---|---|
| x^2, x² | Powers. 2^x and e^x are exponentials |
| sqrt(x), cbrt(x) | Square root and cube root |
| x^(1/3) | Fractional powers. Odd roots of negative numbers stay real |
| sin, cos, tan | Trig functions, in radians or degrees |
| asin, acos, atan | Inverse trig functions |
| sinh, cosh, tanh | Hyperbolic functions |
| ln(x), log(x), log2(x) | Natural log, log base 10, log base 2 |
| abs(x) | Absolute value |
| pi, e | The constants π and e |
Where a function has no real value, like sqrt(x) for negative x or ln(x) at 0, the curve simply stops. It starts again where the function is defined, and the curve is drawn right up to the edge of its domain.
Asymptotes without false lines
A simple plotter connects every pair of neighboring points with a straight line. At an asymptote of tan(x) or 1/x, one point sits far above the view and the next far below, so the plotter draws a vertical line that is not part of the graph.
This calculator checks every large jump before it draws it. It looks at the point halfway between the two, then halfway again, always toward the bigger change. On a steep but unbroken curve like x⁹, the change soon becomes smaller than a pixel, so the points are joined. At an asymptote it never shrinks, so the curve is split into separate branches. The same check stops false lines at jumps, like x/abs(x) at 0.
Finding roots and intersections
A root is an x where f(x) = 0, the place the curve crosses or touches the x-axis. An intersection of two curves is an x where f(x) = g(x), which is a root of f(x) − g(x). The calculator finds both numerically:
- It evaluates the function at 2,000 evenly spaced x values across the visible part of the graph.
- Where two neighbors have opposite signs, it halves the interval until the root is pinned down to the precision of the computer's numbers. A sign change at an asymptote is thrown out, because the value there grows instead of shrinking to 0.
- Where |f(x)| dips to a low point without a sign change, it searches for the bottom of the dip and keeps it if the value there is 0, like x² at x = 0.
Results are shown to 6 significant digits. Only the visible range is searched, so pan or zoom out to find roots outside it. A curve that wiggles faster than the 2,000 sample points, like sin(1/x) near 0, can hide some of its roots; zoom in to see them. For quadratics, the quadratic equation solver gives exact roots with square roots and fractions.
Trace, zoom and the table
Turn on Trace and move along a curve with the mouse, a finger or the arrow keys. The readout below the graph shows x and y at that point; the up and down arrow keys switch between curves. To zoom, scroll, pinch, use the + and − buttons, or double-click a spot. Fit stretches the y-axis so the curves fill the view, and the reset button brings back the starting view, with equal units on both axes in radians.
The table of values starts at the x you choose and goes up in your step, with one column per function. It is handy for checking a point by hand or for filling in a worksheet. Undefined values are marked as such.
How to use the graphing calculator
- 1Type a function of x next to y₁, like x^2 − 4 or sin(2x). Press Add function for up to five curves, or tap an example.
- 2Drag, scroll or pinch to move and zoom. Pick radians or degrees for the trig functions, and turn on Trace to read exact points.
- 3Read the roots, intersections and the table of values below the graph. Download the graph as a PNG or copy a link that keeps your functions and view.
Frequently asked questions
How do I type a function?
Type the right-hand side of y = f(x), like x^2 − 3x + 1 or sin(2x). You can leave out the × sign, so 2x, 3sin(x) and (x + 1)(x − 1) all work. Use ^ for powers, sqrt for square roots, abs for absolute value, ln and log for logarithms, and pi and e for the constants. If you type "y =" in front, it is ignored.
Why is there no vertical line at the asymptotes of tan(x) or 1/x?
Before joining two neighboring points, the graph checks whether the curve really runs between them. It halves the gap again and again: on a steep but continuous curve the jump shrinks, at an asymptote it does not. Where it does not, the line is broken, so tan(x) shows separate branches instead of false vertical lines.
How are roots and intersections found?
Numerically, in the part of the graph you can see. The calculator evaluates each function at 2,000 points across the view, looks for sign changes and narrows each one down by bisection, and it also finds places where the curve only touches the x-axis, like x² at 0. Intersections are the roots of the difference of two functions. Zoom or pan to search a different range.
Should I use degrees or radians?
Radians are the default, so sin(x) repeats every 2π, about 6.28. Switch to DEG to read x as degrees; the x-axis then stretches so the same waves stay in view, and sin(x) repeats every 360. The setting only changes the trig functions.
Can I save or share the graph?
Press Download PNG to save the graph as an image with a legend of your functions. Copy link gives you an address that opens the calculator with the same functions, angle mode and view, so a classmate sees exactly what you see.
Does the graphing calculator work on a phone?
Yes. Drag with one finger to move the graph and pinch with two to zoom. Turn on Trace to slide along a curve with your finger instead, with the coordinates shown below the graph.