Determine which portion of the plane we should shade to show the solution set.
Boundary Line
The boundary line of an inequality can be determined by replacing the inequality symbol with an equals sign.
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Inequality & Boundary Line [0.5em]
y > |x-2|+1 & y = |x-2|+1
We will plot these ordered pairs on a coordinate plane and connect them to get the graph of the given function. Notice that the function is a transformation of the parent function f(x)=|x|, which is V-shaped. Thus, the given function will also be a V-shaped graph.
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.
