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What kind of transformation converts the graph of f(x)=−2(x−9)2−2f(x) = -2(x - 9)^2 - 2 into the graph of g(x)=−2(x−6)2−2g(x) = -2(x - 6)^2 - 2?\newlineChoices:\newline(A) translation 33 units right\newline(B) translation 33 units up\newline(C) translation 33 units down\newline(D) translation 33 units left

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Q. What kind of transformation converts the graph of f(x)=−2(x−9)2−2f(x) = -2(x - 9)^2 - 2 into the graph of g(x)=−2(x−6)2−2g(x) = -2(x - 6)^2 - 2?\newlineChoices:\newline(A) translation 33 units right\newline(B) translation 33 units up\newline(C) translation 33 units down\newline(D) translation 33 units left
  1. Compare functions: Compare the two functions f(x)f(x) and g(x)g(x). The only difference is the expression inside the parentheses: (x−9)(x - 9) in f(x)f(x) and (x−6)(x - 6) in g(x)g(x).
  2. Shift to the right: To go from (x−9)(x - 9) to (x−6)(x - 6), we add 33 to xx. This means the graph of f(x)f(x) is shifted to the right by 33 units to get g(x)g(x).
  3. Vertical component unchanged: The vertical component of the functions, represented by −2-2 outside the parentheses, remains unchanged. So there's no vertical shift.
  4. Correct transformation: The correct transformation is a translation 33 units to the right, which corresponds to choice (A).

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