Question

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

Answer 1

D

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.