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What kind of transformation converts the graph of f(x)=−9∣x+7∣+8f(x) = -9|x + 7| + 8 into the graph of g(x)=−9∣x+7∣g(x) = -9|x + 7|?\newlineChoices:\newline(A) translation 88 units down\newline(B) translation 88 units up\newline(C) translation 88 units left\newline(D) translation 88 units right

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Q. What kind of transformation converts the graph of f(x)=−9∣x+7∣+8f(x) = -9|x + 7| + 8 into the graph of g(x)=−9∣x+7∣g(x) = -9|x + 7|?\newlineChoices:\newline(A) translation 88 units down\newline(B) translation 88 units up\newline(C) translation 88 units left\newline(D) translation 88 units right
  1. Analyze Functions: Analyze the given functions f(x)=−9∣x+7∣+8f(x) = -9|x + 7| + 8 and g(x)=−9∣x+7∣g(x) = -9|x + 7|. Identify the difference between the two functions. The only difference is the constant term +8+ 8 in f(x)f(x) which is not present in g(x)g(x).
  2. Identify Difference: Determine the type of transformation.\newlineThe removal of +8+ 8 from f(x)f(x) to get g(x)g(x) indicates a vertical shift.
  3. Type of Transformation: Determine the direction of the vertical shift.\newlineSince +8+ 8 is removed, the graph moves down by 88 units.
  4. Direction of Shift: Match the transformation with the given choices.\newlineThe graph of f(x)f(x) is shifted 88 units down to get the graph of g(x)g(x).\newlineThis matches choice (A) translation 88 units down.

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