Inequality graphing calculator

Type an inequality and the region that satisfies it is shaded, with a dashed boundary for < and > and a solid one for ≤ and ≥. Add more inequalities and the overlap shows the solution of the system.

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The system

y>x²−4

y≤4−x²2

. The solution is the darker region where both shadings overlap.

How to use the inequality graphing calculator

1
Type an inequality in x and y, such as y > 2x - 1. Use <= and >= for ≤ and ≥.
2
Add each inequality of a system on its own row. The region where all the shadings overlap is the solution.
3
Write compound inequalities in one row: -2 < y < x.
4
Change a region’s colour or opacity from the row’s settings to make the overlap clearer.

Solid or dashed boundary?

The boundary is the curve where the two sides are equal. For a strict inequality (< or >) the boundary is not part of the solution, so it is drawn dashed. For ≤ or ≥ it is included and drawn solid. The calculator does this automatically from the symbol you type.

Which side to shade

By hand, pick a test point that is not on the boundary, usually (0, 0), and substitute it. If the inequality is true there, shade the side containing the point; otherwise shade the other side.

For y > 2x − 1: at (0, 0), 0 > −1 is true, so the region above the line, which contains the origin, is shaded. For curves such as circles the same test works: x² + y² < 9 is true at the origin, so the inside of the circle is shaded.

Exact shading

Many graphers decide each pixel by sampling the inequality at its centre, which can leave ragged edges and miss thin regions. With certified mode on (the default), this calculator uses interval arithmetic to prove which blocks of the screen lie entirely inside or outside the region, fills those exactly, and only decides the remaining edge pixels individually. Thin slivers and sharp corners are shaded correctly.