Graphing a Nonlinear Inequality in Two Variables

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Graph the inequality x^2+y^2≥9.

Steps for Graphing Nonlinear Inequalities in Two Variables

Step 1. Replace the inequality symbol with an equal sign and graph the resulting equation. If the inequality is strict, sketch the graph using dashes. If the inequality is non-strict, sketch the graph using a solid curve. This graph divides the coordinate plane into two or more regions.

Step 2. Choose one test point that does not belong to the graph of the equation from step 1 and determine if it is a solution to the inequality.

Step 3. If the test point is a solution to the inequality, shade the region that contains the test point. If the test point is not a solution to the inequality, shade the region that does not include the test point.

In order to be certain that all of the solution set has been identified, it may be necessary to choose more than one test point when the graph of a nonlinear inequality in two variables divides the coordinate plane into multiple regions.

Step 1. The inequality is non-strict, so we graph the equation x2 + y2 = 9 (which is a circle centered at the origin having a radius of 3 units) using a continuous solid curve.

Step 2. We choose the test point (0, 0), which lies inside the circle.

Step 3. Because the test point (0, 0) is not a solution to the inequality, we shade the region that lies outside of the circle.