Answer:
D. F(x) = (x +3)³ -2
Explanation:
As with most multiple-choice math problems, you can try the different answers to see which is consistent with the information given in the problem. Here, that would mean you evaluate f(-3) to see if you get the value -2.
A. (-3+2)³ -3 = -4 ≠ -2
B. (-3 -3)³ -2 = -218 ≠ -2
C. (-3 -2)³ -3 = -128 ≠ -2
D. (-3 +3)³ -2 = -2 . . . . . . the correct choice
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You are probably expected to understand that F(x) has been translated left 3 units and down 2 units from G(x). (The marked inflection point gives you the clue you need.) The transformation that translation does this is:
F(x) = G(x -h) +k . . . . . G(x) translated by (h, k) units (right, up)
Translation left 3 and down 2 gives you (h, k) = (-3, -2), so ...
F(x) = G(x -(-3)) -2 = G(x +3) -2
F(x) = (x +3)³ -2