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What kind of transformation converts the graph of f(x)=9∣x−8∣+1f(x) = 9|x - 8| + 1 into the graph of g(x)=9∣x−8∣+2g(x) = 9|x - 8| + 2?\newlineChoices:\newline(A) translation 11 unit up\newline(B) translation 11 unit right\newline(C) translation 11 unit left\newline(D) translation 11 unit down

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Q. What kind of transformation converts the graph of f(x)=9∣x−8∣+1f(x) = 9|x - 8| + 1 into the graph of g(x)=9∣x−8∣+2g(x) = 9|x - 8| + 2?\newlineChoices:\newline(A) translation 11 unit up\newline(B) translation 11 unit right\newline(C) translation 11 unit left\newline(D) translation 11 unit down
  1. Compare functions: Compare f(x)f(x) and g(x)g(x) to see the difference.f(x)=9∣x−8∣+1f(x) = 9|x - 8| + 1g(x)=9∣x−8∣+2g(x) = 9|x - 8| + 2The only difference is the constant term at the end.
  2. Determine transformation type: Determine the type of transformation based on the change in the constant term.\newlineThe constant term in g(x)g(x) is 11 unit greater than in f(x)f(x).\newlineThis indicates a vertical shift.
  3. Identify vertical shift direction: Identify the direction of the vertical shift.\newlineSince the constant term increased by 11, the graph moves up.
  4. Match transformation to choices: Match the transformation to the given choices.\newlineThe graph of f(x)f(x) is translated 11 unit up to get g(x)g(x).

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