The boundary line of an inequality can be determined by replacing the inequality symbol with an equal sign.
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Inequality&Boundary Line
y < |x|+6 & y = |x|+6
The graph of this function is the graph of y=|x| after a transformation. Let's first figure out which transformation was involved so that we can graph it.
Vertical Translations
Translation up k units, k>0
y=f(x)+ k
Translation down k units, k>0
y=f(x)- k
Using the table, we can see that there is a vertical translation 6 units up. Applying this transformation to y=|x|, we can draw the boundary line. Because the inequality is strict, the boundary line will be dashed.
Shading the Solution Set
In order to decide which part of the plane to shade, we can test a point which is not on the boundary line. Let's test the point ( 0, 0).
If the point satisfies the inequality, we shade the region that contains the point. Otherwise, we shade the region that does not contain the point.
