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What kind of transformation converts the graph of f(x)=10∣x−1∣+9f(x) = 10|x - 1| + 9 into the graph of g(x)=10∣x−1∣+10g(x) = 10|x - 1| + 10?\newlineChoices:\newline(A) translation 11 unit down\newline(B) translation 11 unit left\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−1∣+9f(x) = 10|x - 1| + 9 into the graph of g(x)=10∣x−1∣+10g(x) = 10|x - 1| + 10?\newlineChoices:\newline(A) translation 11 unit down\newline(B) translation 11 unit left\newline(C) translation 11 unit up\newline(D) translation 11 unit right
  1. Analyze Functions: Analyze the given functions f(x)f(x) and g(x)g(x).f(x)=10∣x−1∣+9f(x) = 10|x - 1| + 9g(x)=10∣x−1∣+10g(x) = 10|x - 1| + 10Compare 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.\newlinef(x)f(x) has a constant term of +9+9, while g(x)g(x) has a constant term of +10+10.
  3. Determine Transformation Direction: Determine the direction of the transformation. Since the constant term in g(x)g(x) is 11 unit greater than the constant term in f(x)f(x), this indicates a vertical shift.
  4. Determine Vertical Shift: Determine the magnitude and direction of the vertical shift. The constant term increased by 11, which means the graph of f(x)f(x) is shifted up by 11 unit to become the graph of g(x)g(x).
  5. Match Transformation: Match the transformation with the given choices.\newlineThe graph of f(x)f(x) is shifted 11 unit up to become the graph of g(x)g(x), which corresponds to choice (C) translation 11 unit up.

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