The simple way to answer this is to take a few points from the graph and compare it with each option.
Let's take points at x = 0, 1, 2
From graph,
When x = 0, y = 1, hence the point is (0, 1)
When x = 1, y = 0, hence the point is (1, 0)
When x = 2, y = -1, hence the point is (2, -1)
Now, put the same x values in the given options to evaluate the output.
For x = 0, the pair should be (0, 1),
1) |x + 5| + 4 = |0 + 5| + 4 = |5| + 4 = 9 => (0, 9) Not true
2) |x + 5| - 4 = |0 + 5| - 4 = |5| - 4 = 1 => (0, 1) True
3) |x - 5| + 4 = |0 - 5| + 4 = |-5| + 4 = 5 + 4 = 9 => (0, 9) Not True
4) |x - 5| - 4 = |0 - 5| - 4 = |-5| - 4 = 5 - 4 = 1 => (0, 1) True
Hence, 2nd and 4th options can be true. Now, evaluate these two options with some other point.
For x = 1, the pair should be (1, 0),
2) |x + 5| - 4 = |1 + 5| - 4 = |6| - 4 = 2 => (0, 2) Not True
4) |x - 5| - 4 = |1 - 5| - 4 = |-4| - 4 = 4 - 4 = 1 => (0, 0) True
Hence, the 4th option is true.
