2-7 graphing inequalities objectives students will be able to: 1) graph linear inequalities 2) graph...
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2-7 Graphing Inequalities
ObjectivesStudents will be able to:
1) graph linear inequalities2) graph absolute value inequalities
Linear inequalities
• A linear inequality resembles a linear equation, but with an inequality symbol, rather than an equal sign.
• The graph of a linear inequality is the region of the graph in which every point in the region satisfies the inequality. This region gets shaded.
A linear inequality can be graphed by following these steps:
1) Determine whether the boundary (the line) should be solid or dashed. Then graph the boundary.
or means solid boundary< or > means dashed boundary2) Choose a point not on the boundary and
test it in the inequality. [(0, 0) is my suggestion] 3) If a true inequality results, shade the region containing your test point.
If a false inequality results, shade the other region.
Example 1: Graph each inequality.
Step 1: Graph y=2x+1; However, since the symbol is >, the line should be dashed.Step 2: Test (0, 0)
Step 3: Shade your region!
Try this.
Maintain your composure, and give this a shot.
Try this on for size.
Absolute value inequalities
• Now that you are having the most fun you have ever had in your entire life, EVER, let’s look at absolute value inequalities.
• Graphing absolute value inequalities is done following the same procedure as graphing linear inequalities. Start by graphing the absolute value function (same rules for solid or dashed). Then pick a test point, and finally shade the region that works.
Example 2: Graph each absolute value inequality.
Try this.
One more.