Question

Which of the following graph shows the graph of the inequality $y\le |x+2|?$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Best way to solve such problem is by checking graph for different values of x.
When x = 0, y = 2;
and when x = -2 , y = 0.
Check these two points on the different graph.
Only graph (d) is true for both these points, hence is the correct answer.

Alternatively:
For x = -2, (x + 2) is equal to zero.
When (x+2) is positive, y = (x+2) .
When (x+2) is negative, y = -(x+2) => x + y = -2.
Graph (d) contains both the functions y = (x+2) and y = -(x+2).