Question

Which absolute value inequality is modeled by this graph?

A.
y < |x − 2 | − 2

B.
y > |4x + 2| − 2

C.
y > |2x − 4| − 2

D.
y < |3x − 6| − 2

Answer 1

I think it is D because the boundaries is a dash line to indicate points on the boundaries are not part of the shaded answer.

Answer 2

Answer: Choice D

y < |3x − 6| − 2

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Step-by-step 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