Write an inequality for the graph. a) y ≥ |x + 5| + 5 b) y ≤ |x – 5| – 5 c) y ≥ |x – 5| + 5 d) y ≤ |x – 5| + 5

D

Step-by-step explanation:

The boundary line for the inequality is translated 5 units to the right and 5 units up graph of the function y=|x|. This translation gives you the function y=|x-5|+5.

This boundary line is solid, then the inequality should  contain notion "or equal to" (the sign of inequality should be ≤ or ≥).

You can see that the origin belongs to the sgaded region, then its coordinates satisfy the inequality. Since 0≤|0-5|+5  (0≤10), then correct choice is D.