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What kind of transformation converts the graph of f(x)=7∣x−4∣−2f(x) = 7|x - 4| - 2 into the graph of g(x)=7∣x+2∣−2g(x) = 7|x + 2| - 2?\newlineChoices:\newline(A) translation 66 units right\newline(B) translation 66 units down\newline(C) translation 66 units up\newline(D) translation 66 units left

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Q. What kind of transformation converts the graph of f(x)=7∣x−4∣−2f(x) = 7|x - 4| - 2 into the graph of g(x)=7∣x+2∣−2g(x) = 7|x + 2| - 2?\newlineChoices:\newline(A) translation 66 units right\newline(B) translation 66 units down\newline(C) translation 66 units up\newline(D) translation 66 units left
  1. Identify Vertex of f(x)f(x): Identify the vertex of the function f(x)=7∣x−4∣−2f(x) = 7|x - 4| - 2. The vertex of the absolute value function f(x)=a∣x−h∣+kf(x) = a|x - h| + k is (h,k)(h, k). For f(x)=7∣x−4∣−2f(x) = 7|x - 4| - 2, h=4h = 4 and k=−2k = -2. Vertex of f(x)f(x): (4,−2)(4, -2)
  2. Identify Vertex of g(x)g(x): Identify the vertex of the function g(x)=7∣x+2∣−2g(x) = 7|x + 2| - 2. The vertex of the absolute value function g(x)=a∣x−h∣+kg(x) = a|x - h| + k is (h,k)(h, k). For g(x)=7∣x+2∣−2g(x) = 7|x + 2| - 2, h=−2h = -2 and k=−2k = -2. Vertex of g(x)g(x): (−2,−2)(-2, -2)
  3. Determine Transformation Type: Determine the type of transformation from f(x)f(x) to g(x)g(x). The transformation involves a horizontal shift from the vertex of f(x)f(x) to the vertex of g(x)g(x). The shift is from (4,−2)(4, -2) to (−2,−2)(-2, -2), which is a movement of 66 units to the left.

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