Answer :

Solution :

From the given graph,

When x = 0, y = 0

x = ±1, y = -1

x = ±2, y = 0

x = ±3, y = 0

Now, let check the given options for the values of x = 0, ±1, ±2, ±3

For x = 0:

y = ||x| + 1| − 2 = -1 (fails)

y = ||x| − 1| − 1 = 0

y = ||x| + 1| − 1 = 0

y = ||x − 1| − 1| = 0

For x = ±1:

y = ||x| − 1| − 1 = -1

y = ||x| + 1| − 1 = 1 (fails)

y = ||x − 1| − 1| = 1 (fails)

For x = ±2:

y = ||x| − 1| − 1 = 0

For x = ±3:

y = ||x| − 1| − 1 = 1

Only y = ||x| − 1| − 1 satisfies the given graph