Equation Grapher

A graph plots every point \((x, y)\) where \(y\) equals the value of the expression for that \(x\). For \(y = x^2\), the point \((2, 4)\) is on the graph because \(2^2 = 4\). Connecting all such points produces the curve you see.

The horizontal axis shows \(x\) values and the vertical axis shows \(y\) values. The numbers at the edges (set by the X Min/Max and Y Min/Max inputs) tell you the visible range. Tick labels along each axis mark intermediate values. Use the range inputs to zoom into a region of interest, or scroll the mouse wheel over the canvas.

Use x as the variable, ^ for exponents, and * for multiplication (or omit it between a number and a variable, like 3x). Standard math functions work by name: sin(x), cos(x), tan(x), sqrt(x), abs(x), log(x), exp(x). Constants pi and e are recognized. So sin(x) * cos(x), sqrt(abs(x)), and exp(-x^2/2) are all valid.

Points where the expression returns NaN, Infinity, or -Infinity are simply skipped. For \(\dfrac{1}{x}\), the grapher draws two separate branches with no line crossing through \(x = 0\). For \(\tan(x)\), the asymptotes appear as gaps. The line you see is connected only between points where the function actually has a finite value.

Not directly. This grapher plots \(y = f(x)\), so each \(x\) gives at most one \(y\). A vertical line like \(x = 3\) isn't a function of \(x\), and an implicit equation like \(x^2 + y^2 = 1\) (a circle) requires solving for \(y\) in pieces. For the circle, you'd plot \(\sqrt{1 - x^2}\) and \(-\sqrt{1 - x^2}\) as two separate graphs to see the full shape.