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What kind of transformation converts the graph of f(x)=2∣x−3∣+7f(x) = 2|x - 3| + 7 into the graph of g(x)=2∣x+7∣+7g(x) = 2|x + 7| + 7?\newlineChoices:\newline(A) translation 1010 units left\newline(B) translation 1010 units down\newline(C) translation 1010 units right\newline(D) translation 1010 units up

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Q. What kind of transformation converts the graph of f(x)=2∣x−3∣+7f(x) = 2|x - 3| + 7 into the graph of g(x)=2∣x+7∣+7g(x) = 2|x + 7| + 7?\newlineChoices:\newline(A) translation 1010 units left\newline(B) translation 1010 units down\newline(C) translation 1010 units right\newline(D) translation 1010 units up
  1. Identify Vertex f(x)f(x): Identify the vertex of the function f(x)=2∣x−3∣+7f(x) = 2|x - 3| + 7. The vertex is at (3,7)(3, 7) because the absolute value function has its vertex where the expression inside the absolute value is zero.
  2. Identify Vertex g(x)g(x): Identify the vertex of the function g(x)=2∣x+7∣+7g(x) = 2|x + 7| + 7. The vertex is at (−7,7)(-7, 7) because the absolute value function has its vertex where the expression inside the absolute value is zero.
  3. Determine Horizontal Shift: Determine the horizontal shift between the vertices of f(x)f(x) and g(x)g(x). The shift is from (3,7)(3, 7) to (−7,7)(-7, 7), which is 1010 units to the left.
  4. Match Transformation: Match the transformation with the given choices.\newlineThe transformation is a translation 1010 units left, which corresponds to choice (A)(A).

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