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What kind of transformation converts the graph of f(x)=4∣x+1∣−3f(x) = 4|x + 1| - 3 into the graph of g(x)=4∣x+9∣−3g(x) = 4|x + 9| - 3?\newlineChoices:\newline(A) translation 88 units down\newline(B) translation 88 units up\newline(C) translation 88 units left\newline(D) translation 88 units right

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Q. What kind of transformation converts the graph of f(x)=4∣x+1∣−3f(x) = 4|x + 1| - 3 into the graph of g(x)=4∣x+9∣−3g(x) = 4|x + 9| - 3?\newlineChoices:\newline(A) translation 88 units down\newline(B) translation 88 units up\newline(C) translation 88 units left\newline(D) translation 88 units right
  1. Identify Vertex of f(x)f(x): Identify the vertex of the function f(x)=4∣x+1∣−3f(x) = 4|x + 1| - 3. The vertex of the absolute value function f(x)=4∣x+h∣+kf(x) = 4|x + h| + k is (−h,k)(-h, k). For f(x)=4∣x+1∣−3f(x) = 4|x + 1| - 3, h=−1h = -1 and k=−3k = -3. Vertex of f(x)f(x): (−1,−3)(-1, -3)
  2. Identify Vertex of g(x)g(x): Identify the vertex of the function g(x)=4∣x+9∣−3g(x) = 4|x + 9| - 3. Similarly, for g(x)=4∣x+h∣+kg(x) = 4|x + h| + k, h=−9h = -9 and k=−3k = -3. Vertex of g(x)g(x): (−9,−3)(-9, -3)
  3. Determine Transformation Type: Determine the type of transformation from f(x)f(x) to g(x)g(x). The change in the hh-value from f(x)f(x) to g(x)g(x) is from −1-1 to −9-9, which is a shift of 88 units to the left. There is no change in the kk-value, so there is no vertical shift. Transformation: translation 88 units left

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