Answer: Choice D
y < |3x − 6| − 2
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Explanation:
Writing y < |3x − 6| − 2 is the same as y < 3|x − 2| − 2 when factoring out the GCF from the absolute value brackets.
Let's look at a breakdown of each piece of y < 3|x − 2| − 2
- The 3 out front means "vertically stretch by a factor of 3".
- The x-2 means we shift 2 units to the right.
- The -2 at the very end means "shift 2 units down"
If we started with the parent V shaped graph of y = |x|, and applied those transformations listed above in the bullet points, then we'd get the boundary shown in the graph. The boundary is a dashed line to indicate "points on the boundary are NOT part of the shaded solution set". If we had an "or equal to" then we would include boundary points with a solid boundary line.
We shade below the dashed boundary to complete the shaded region for y < |3x − 6| − 2 aka y < 3|x − 2| − 2
