Graphing Calculator
Type one or more functions of x and see them plotted instantly. Zoom, pan, hover to read exact coordinates, and get every intersection point and a table of values.
Try 2x^2 - 3, sin(x)/x, sqrt(abs(x)), ln(x), e^(-x^2), 1/x or tan(x). Implicit multiplication like 3x or 2sin(x) works.
Intersection points in view
Table of values
How to use the Graphing Calculator
- Type a function of x in the first row, for example x^2 - 4 or 2sin(x).
- Add more functions with + Add function. Pick a color with the round swatch, and use the eye button to show or hide a graph.
- Press Plot (or just keep typing, the graph updates live).
- Explore the graph: drag to pan, scroll or pinch to zoom, and hover or tap to read coordinates. Reset view returns to −10…10.
- Read the intersections listed under the graph, and set x from, x to and step to build a table of values you can copy.
Supported functions and syntax
| Type | Meaning | Example |
|---|---|---|
+ − * / | Add, subtract, multiply, divide | 3x - 1, x/2 |
^ | Power (right to left: 2^3^2 = 2^9) | x^3, 2^x, e^(-x^2) |
sqrt, cbrt, abs | Square root, cube root, absolute value | sqrt(x + 4) |
sin cos tan, sec csc cot | Trigonometry in radians | 2sin(3x) |
asin acos atan, sinh cosh tanh | Inverse and hyperbolic functions | atan(x) |
ln, log, log(x, b), exp | Natural log, log base 10, log base b, e^x | log(x, 2) |
floor ceil round sign | Rounding and sign | floor(x) |
pi, e | Constants π ≈ 3.14159 and e ≈ 2.71828 | sin(pi x) |
Write -x^2 to mean −(x²): powers are applied before the minus sign, exactly as in algebra. Use brackets whenever you are unsure, for example (-x)^2.
Finding where two graphs intersect: a worked example
Two graphs meet where their y-values are equal. For y₁ = x² and y₂ = x + 2, set them equal: x² = x + 2, so x² − x − 2 = 0. This factors as (x − 2)(x + 1) = 0, giving x = 2 and x = −1. Substituting back into y₂ gives the points (2, 4) and (−1, 1), which is exactly what the calculator lists for the default functions.
The tool does the same thing numerically for any pair of functions: it looks at the difference d(x) = y₁(x) − y₂(x) across the visible range, spots every place where d changes sign, and then halves the interval again and again (the bisection method) until the crossing is pinned down. That is why it also works for equations you cannot solve by hand, such as cos(x) = x, whose only solution is x ≈ 0.739085.
Reading a graph: key features to look for
| Feature | What it means | How to find it here |
|---|---|---|
| x-intercepts (roots) | Values of x where f(x) = 0 | Add the function y = 0 and read the intersection points |
| y-intercept | The value f(0) | Hover at x = 0 or start the table at 0 |
| Vertical asymptote | The graph shoots off to ±∞, e.g. 1/x at x = 0 | Look for a break in the curve |
| Maximum / minimum | Highest or lowest point in a region | Zoom in and hover; the table with a small step narrows it down |
| Period | Distance after which a curve repeats, 2π for sin(x) | Compare x-values of matching peaks |
Transformations of a function
Plotting a base function next to a changed version is the fastest way to understand transformations. Starting from y = f(x): f(x) + k moves the graph up by k, f(x − h) moves it right by h, a·f(x) stretches it vertically by a factor a (and flips it when a is negative), and f(b·x) squeezes it horizontally by a factor b. Try x^2, (x - 3)^2 + 1 and -0.5x^2 together to see all three at once.
Frequently asked questions
How do I type powers, roots and logarithms?
Use ^ for powers (x^3, 2^x), sqrt(x) for square roots, cbrt(x) for cube roots, abs(x) for absolute value, ln(x) for the natural logarithm, log(x) for log base 10 and log(x, b) for any base. Constants pi and e are built in.
Do I need to type the multiplication sign?
No. Implicit multiplication works, so 2x, 3x^2, 2sin(x), x(x - 1) and 4pi are all understood. You can still type * if you prefer.
Are angles in degrees or radians?
Trigonometric functions use radians, which is the standard for graphing. To graph sine of x degrees, type sin(x*pi/180).
How are intersection points found?
The calculator samples the difference between each pair of visible functions across the current view, finds every sign change and then narrows each one down by bisection to about 15 significant digits. Touching points where the graphs meet without crossing are found by a minimum search. Only points inside the current view are listed, so zoom out to find more.
Why is there a gap in the graph of tan(x) or 1/x?
Those functions have vertical asymptotes where they jump from very large positive to very large negative values. The plotter detects these jumps and lifts the pen instead of drawing a misleading vertical line.
Why does my function show nothing for some x values?
Values outside a function's domain are skipped, for example sqrt(x) for negative x or ln(x) for x ≤ 0. The table shows – for those x values.
Can I save or share the graph?
Press Download PNG to save the current view as an image. Your functions are remembered in this browser, so they are still there next time you open the page.