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What kind of transformation converts the graph of f(x)=−10∣x−7∣−7f(x) = -10|x - 7| - 7 into the graph of g(x)=−10∣x−7∣−8g(x) = -10|x - 7| - 8?\newlineChoices:\newline(A) translation 11 unit left\newline(B) translation 11 unit down\newline(C) translation 11 unit up\newline(D) translation 11 unit right

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Q. What kind of transformation converts the graph of f(x)=−10∣x−7∣−7f(x) = -10|x - 7| - 7 into the graph of g(x)=−10∣x−7∣−8g(x) = -10|x - 7| - 8?\newlineChoices:\newline(A) translation 11 unit left\newline(B) translation 11 unit down\newline(C) translation 11 unit up\newline(D) translation 11 unit right
  1. Analyze Functions: Analyze the given functions.\newlineWe have f(x)=−10∣x−7∣−7f(x) = -10|x - 7| - 7 and g(x)=−10∣x−7∣−8g(x) = -10|x - 7| - 8. Compare the two functions to determine the type of transformation.
  2. Identify Change: Identify the change in the functions.\newlineThe only difference between f(x)f(x) and g(x)g(x) is the constant term at the end of the equation. f(x)f(x) has −7-7, and g(x)g(x) has −8-8.
  3. Determine Transformation Direction: Determine the direction of the transformation. Since the change is in the constant term, and it is a decrease from −7-7 to −8-8, this indicates a vertical shift.
  4. Calculate Transformation Magnitude: Calculate the magnitude of the transformation.\newlineThe change from −7-7 to −8-8 is a decrease by 11 unit. Therefore, the graph of f(x)f(x) is shifted down by 11 unit to become g(x)g(x).
  5. Match Transformation with Choices: Match the transformation with the given choices.\newlineThe graph of f(x)f(x) is shifted 11 unit down to become g(x)g(x). This matches choice (B) translation 11 unit down.

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