An inequality describes a region rather than a single curve. The boundary shows where equality holds, and the shading shows all points that satisfy the inequality.
Step 1: graph the boundary
Replace the inequality symbol temporarily with equality. For y≥x^2, the boundary is the parabola y=x^2.
Step 2: decide whether the boundary is included
- Use a solid boundary for
≤or≥. - Use a dashed boundary for
<or>.
The boundary is part of the solution only when equality is allowed.
Step 3: determine the shaded side
For an inequality already written as y compared with a function:
y>f(x)means shade above the graph.y<f(x)means shade below the graph.
Thus y≥x^2 shades the region on and above the parabola.
Use a test point when needed
For a relation such as 2x+3y<6, draw the boundary 2x+3y=6 and test a point not on the line, often (0,0). Since 0<6 is true, shade the side containing the origin.
Implicit inequalities
The relation x^2+y^2≤9 describes the disk of radius 3 centered at the origin. Use Equation / Inequality mode when the boundary cannot be represented as one ordinary y=f(x) function.
Graph shading tools
You can enter an inequality directly where supported or create boundary functions and use the Graph Shading tool. Choose the boundary objects, interval, color, opacity, and pattern.
Interval restrictions
Sometimes only part of a region is needed. Set the x- or y-interval carefully. An interval restriction does not change the mathematical boundary; it limits where the shading is displayed.
Common mistakes
- Using a solid line for a strict inequality.
- Shading above when the relation requires below.
- Testing a point that lies on the boundary.
- Forgetting that multiplying or dividing by a negative number reverses the inequality sign.
- Using a function mode for a relation that is not single-valued.
Practice examples
y<2x+1y≥x^2-4x^2+y^2≤9|x|+|y|<4
Open Graph Shading and try these inequalities →
For a region bounded by two curves, read how to shade between two graphs.