Function Grapher
Plot up to 4 functions with zoom, pan, values on tap and PNG download
Runs entirely in your browser. Nothing you type or upload is sent to us or stored.
Results are for general guidance. Please check anything important before relying on it. Terms of use
How to Use
- Type a function next to y₁ =, for example sin(x), x^2 − 4 or 1/x. Use add function or the quick buttons (sin x, x², 1/x, eˣ, |x| and more) to draw up to four curves, each in its own colour.
- Drag the graph to move around. Zoom with the mouse wheel, by pinching on a phone, or with the zoom buttons. The circular-arrow button resets the view.
- For an exact window, type x min, x max, y min and y max under the graph and press Enter.
- Hover over the graph, or tap it on a phone, to read x and the value of every function at that point. Tap PNG to download the graph as an image.
Plot graphs of functions online
This function grapher draws y = f(x) for up to four functions at once, in different colours, on a grid with labelled axes. It is meant for the moments when you want to see a function rather than work it out: checking where a parabola cuts the x-axis, comparing sin x with cos x, or seeing why tan x breaks into pieces. You can move and zoom freely, read exact values by hovering or tapping, and save the picture as a PNG for notes or an assignment.
What you can type
| To get | Type |
|---|---|
| x², x³ | x^2, x^3 (or x², x³) |
| √x | sqrt(x) or √x |
| |x| | abs(x) or |x| |
| sin x, cos x, tan x | sin(x), cos x, tan(x) |
| Natural log, log base 10 | ln(x), log(x) |
| eˣ, π | e^x, pi |
| 2 × x, 3 × sin x | 2x, 3sin(x) |
You can also start with "y =" or "f(x) =", which is ignored. Trigonometric functions use radians, so sin x crosses zero at x = π ≈ 3.14, not at 180.
Reading a graph: three examples
A parabola. Plot y = x² − 4x + 3. It crosses the x-axis at x = 1 and x = 3, the roots of x² − 4x + 3 = 0, and its lowest point is (2, −1). Hovering at x = 2 shows y = −1. Add y = −x² + 4x − 3 and you get the same parabola flipped upside down.
Asymptotes. y = 1/x has no value at x = 0. As x gets close to 0 from the right, y shoots up; from the left, it drops. The grapher breaks the line there instead of drawing a false vertical stroke, and does the same for tan x at x = ±π/2, ±3π/2 and so on.
Comparing growth. Plot x², 2^x and e^x together and zoom out. The curves y = x² and y = 2^x meet at x = 2 and x = 4. In between, x² is larger, but after x = 4 the exponential 2^x stays ahead and pulls away fast. This is the "exponential beats polynomial" idea that shows up in limits.
Graphs worth knowing for Class 11 and 12
- Modulus function |x|: a V shape with its corner at the origin.
- Greatest integer function: type floor(x) to see the steps.
- sin x and cos x: waves between −1 and 1 with period 2π. cos x is sin x shifted left by π/2.
- eˣ and ln x: mirror images of each other in the line y = x (add y = x to see it).
- Inverse trig: asin(x) exists only for −1 ≤ x ≤ 1, which is its domain.
How the drawing works
The grapher works out each function at roughly one and a half points per pixel across the screen and joins neighbouring points with straight lines. Where a function has no real value (the square root of a negative number, the log of 0) it leaves a gap. Where the value jumps from above the screen to below it between two neighbouring points, it treats that as an asymptote and lifts the pen. The grid spacing is always a "nice" step of 1, 2 or 5 times a power of ten, so the labels stay readable however far you zoom.
Tips
- To find where two curves meet, plot both and hover near the crossing until their values match.
- Very narrow features (such as sin(100x)) can look jagged at a wide zoom. Zoom in to see the true shape.
- The PNG includes the legend, so the downloaded image shows which colour is which function.