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What kind of transformation converts the graph of f(x)=−9∣x+6∣+2f(x) = -9|x + 6| + 2 into the graph of g(x)=−9∣x+6∣−8g(x) = -9|x + 6| - 8?\newlineChoices:\newline(A) translation 1010 units down\newline(B) translation 1010 units left\newline(C) translation 1010 units up\newline(D) translation 1010 units right

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Q. What kind of transformation converts the graph of f(x)=−9∣x+6∣+2f(x) = -9|x + 6| + 2 into the graph of g(x)=−9∣x+6∣−8g(x) = -9|x + 6| - 8?\newlineChoices:\newline(A) translation 1010 units down\newline(B) translation 1010 units left\newline(C) translation 1010 units up\newline(D) translation 1010 units right
  1. Analyze Functions: Analyze the given functions.\newlineWe have f(x)=−9∣x+6∣+2f(x) = -9|x + 6| + 2 and g(x)=−9∣x+6∣−8g(x) = -9|x + 6| - 8. \newlineNotice that the only difference between f(x)f(x) and g(x)g(x) is the constant term at the end of the function.
  2. Type of Transformation: Determine the type of transformation.\newlineSince the only change is in the constant term, and the change is from +2+2 to −8-8, this indicates a vertical shift.
  3. Calculate Vertical Shift: Calculate the amount of vertical shift.\newlineThe change in the constant term is from +2+2 to −8-8, which is a decrease of 1010 units.\newlineTo find the amount of shift: −8−(+2)=−10-8 - (+2) = -10.\newlineThis means the graph has shifted 1010 units down.
  4. Match with Choices: Match the transformation with the given choices.\newlineThe graph has shifted 1010 units down, so the correct choice is (A) translation 1010 units down.

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