Type y=f(x) to draw function curves instantly, with multiple functions, zoom and pan, parameter sliders, zeros/intersections/derivative analysis and PNG/SVG export
Twelve built-in presets cover linear, quadratic, reciprocal, trigonometric, exponential and logarithmic functions — click one to plot it instantly, and overlay up to six curves with individual visibility.
Zoom in on the cursor position and drag to move the viewport. Axis ticks and grid lines are recalculated automatically, so inspecting local detail is effortless.
Three built-in sliders for a, b and c let you watch a family of curves such as y=a·sin(b·x) change in real time, making parameter effects intuitive.
The tool automatically finds every zero, the intersection points between functions, and local maxima and minima, listing them in the analysis panel.
Enter x₀ to see each function's value and derivative at that point, and draw the tangent line to build intuition about instantaneous rate of change.
PNG is exported at high resolution, while SVG is a vector format that scales without loss, ready for papers, slides and print.
Type y=f(x) into a function box, for example sin(x) or x^2/4-1. Implicit multiplication such as 2x and 3sin(x) works too, or click a "Common functions" button above to plot sine, exponential, logarithm and more in one click.
Scroll the wheel to zoom and drag the mouse to pan, or click "Reset view" to return to the default range. Grid and labels can be toggled at any time.
If the expression contains a, b or c, drag the sliders on the right to reshape the curve instantly, a great way to explore how parameters affect a graph.
The analysis panel lists zeros, intersections and extrema. Enter x₀ to inspect derivatives and the tangent line, then click "Export PNG" or "Export SVG" to save.
Sketch the graph from a problem, check zeros and extrema, and verify conclusions quickly
Drop a vector SVG into slides so it stays sharp at any size while explaining function behaviour
Export clean high-resolution figures for model curves, error functions and fitting results
Inspect transfer functions, decay curves and response functions at a glance
Drag the parameter sliders to connect "parameter" with "shape" in a hands-on way
Produce clean, readable function figures for maths articles, videos and blogs
A function graph is the curve formed by all points (x, y) that satisfy y=f(x) in the Cartesian plane. It turns an abstract relationship into a shape you can see, letting you read off increasing and decreasing behaviour, zeros, extrema and symmetry at a glance. It is one of the most effective ways to study functions.
This tool follows maths textbooks and programming languages and uses radians, defined as the ratio of arc length to radius. 180° equals π radians, so sin(pi/2)=1 and cos(pi)=-1. To enter an angle in degrees, convert first: 30° = pi/6 ≈ 0.5236 and 45° = pi/4 ≈ 0.7854.
The tool samples the visible range densely. When two neighbouring samples have opposite signs the curve has crossed the axis, and the bisection method then halves the interval repeatedly to converge on the true zero. Subtracting one function from another and finding zeros gives the intersection points, while extrema are located where the numerical derivative (a central difference) changes sign. Results are numerical approximations shown to 4 significant digits.
PNG is a raster format and becomes jagged when scaled up. SVG is vector-based, describing the image with lines and text, so it stays perfectly sharp at any size, takes little space, and can be placed directly into Word, PowerPoint or LaTeX. Use PNG for bitmaps such as chat messages, and SVG for print or large displays.
| Category | Syntax | Notes and examples |
|---|---|---|
| Basic operators | + - * / ^ % |
Add, subtract, multiply, divide, power, remainder, e.g. 2^10, 7%3 |
| Parentheses | ( ) |
Group expressions, e.g. (x+1)*(x-2) |
| Implicit multiplication | 2x / 3sin(x) |
The multiply sign may be omitted between a number and a variable or function |
| Constants | pi / e |
π ≈ 3.14159 and Euler's number e ≈ 2.71828 |
| Variable and parameters | x / a b c |
x is the independent variable; a, b and c are driven by the sliders |
| Trigonometric | sin cos tan |
Radians; inverses are asin acos atan |
| Hyperbolic | sinh cosh tanh |
Inverses are asinh acosh atanh |
| Exponential and log | exp ln log log2 |
ln is natural log, log(x) is base 10, log(x,b) is base b |
| Other common | sqrt cbrt abs sign |
Square root, cube root, absolute value, sign function |
| Rounding and aggregation | floor ceil round min max |
For example max(sin(x), 0.5) takes the larger of the two |