Graphing Calculator

How a graph represents a function

A function turns each input $x$ into one output $y$. Its graph is every point $(x,y)$ that satisfies the rule, drawn on a coordinate grid. A graph shows behaviour that is hard to spot in a formula: where the function is zero, where it rises and falls, and what happens for very large or very small $x$.

The plotter samples hundreds of $x$ values across the visible window, computes $y$ for each one and joins the points. Where a function is undefined — at $x=2$ in $y=\frac{1}{x-2}$, for example — the curve is broken rather than joined across the gap.

How to use the graphing calculator

1. Type a function after $y=$ — for example x^2 - 4, sin(x) or 1/(x - 2). Multiplication can be implied: 2x and 3sin(x) both work.
2. Add up to four functions to compare them. Each gets its own colour, and the eye button hides a curve without deleting it.
3. Drag to pan, zoom with the + and − buttons (or pinch, or click the graph and scroll), and hover to read coordinates on each curve. For exact intercepts, turning points or intersections, ask the AI solver on this page.

Features worth looking for

• x-intercepts: where the curve crosses the $x$-axis — the solutions of $f(x)=0$.
• y-intercept: the value $f(0)$, where the curve crosses the $y$-axis.
• Turning points: local maxima and minima, where the graph changes from rising to falling.
• Asymptotes: lines the curve approaches but never reaches, common in rational functions.
• Intersections: where two curves meet, which solves the equation $f(x)=g(x)$.

Supported functions

Use + - * / and ^ for powers, with brackets where needed. The plotter understands sin, cos, tan, sec, csc, cot, asin, acos, atan, sinh, cosh, tanh, sqrt, cbrt, abs, ln (natural log), log (base 10), exp, floor and ceil, plus the constants pi and e. Angles are in radians.

Worked example: $y=x^2-4$

1. y-interceptSet $x=0$: $y=-4$, so the curve crosses the $y$-axis at $(0,-4)$.
2. x-interceptsSet $y=0$: $x^2=4$, so $x=-2$ or $x=2$.
3. VertexThe graph of $y=x^2$ has its lowest point at the origin. Subtracting 4 shifts it down, so the vertex is $(0,-4)$.
4. ShapeThe coefficient of $x^2$ is positive, so the parabola opens upward and is symmetric about the line $x=0$.

Common mistakes to avoid

Related calculators

• Solve for XLinear and multi-step equations
• Quadratic equationsRoots, discriminant and formula
• Systems of equationsSubstitution and elimination
• DerivativesPower, product, quotient and chain rules

Questions students ask