Answer: The answer is (D). y = |x + 6| - 3.
Step-by-step explanation: We are given four options of functions and we are to select which one is graphed in the given figure.
From the graph, we have
f(-6) = -3, f(-3) = f(-9) = 0.
From option (A) y=|x-6|+4, we have
f(-6) = 16, -8 ≠ -3. So, this option is not correct.
From option (B) y=|x-6|-3, we have
f(-6) = 9, -15 ≠ -3, so this option is also incorrect.
From option (C) y=|x+6|+3, we have
f(-6) = 3 ≠ -3, so this option is again incorrect.
From option (D) y=|x+6|-3, we have
f(-6) = -3, f(-3) = 0 and f(-9) = 0.
So, this option is correct.
Thus, the correct option is (D).
