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What kind of transformation converts the graph of f(x)=−8∣x−6∣+9f(x) = -8|x - 6| + 9 into the graph of g(x)=−8∣x−2∣+9g(x) = -8|x - 2| + 9?\newlineChoices:\newline(A) translation 44 units up\newline(B) translation 44 units right\newline(C) translation 44 units left\newline(D) translation 44 units down

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Q. What kind of transformation converts the graph of f(x)=−8∣x−6∣+9f(x) = -8|x - 6| + 9 into the graph of g(x)=−8∣x−2∣+9g(x) = -8|x - 2| + 9?\newlineChoices:\newline(A) translation 44 units up\newline(B) translation 44 units right\newline(C) translation 44 units left\newline(D) translation 44 units down
  1. Identify Vertex f(x)f(x): Identify the vertex of f(x)=−8∣x−6∣+9f(x) = -8|x - 6| + 9.\newlineVertex of f(x)f(x): (6,9)(6, 9)
  2. Identify Vertex g(x)g(x): Identify the vertex of g(x)=−8∣x−2∣+9g(x) = -8|x - 2| + 9.\newlineVertex of g(x)g(x): (2,9)(2, 9)
  3. Calculate Horizontal Shift: Calculate the horizontal shift between the vertices of f(x)f(x) and g(x)g(x).\newlineShift: 6−2=46 - 2 = 4 units to the left
  4. Match Calculated Shift: Match the calculated shift with the given choices.\newlineThe graph shifts 44 units left, so the answer is (C) translation 44 units left.

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