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What kind of transformation converts the graph of f(x)=4∣x−8∣+8f(x) = 4|x - 8| + 8 into the graph of g(x)=4∣x−8∣−1g(x) = 4|x - 8| - 1?\newlineChoices:\newline(A) translation 99 units down\newline(B) translation 99 units up\newline(C) translation 99 units right\newline(D) translation 99 units left

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Describe function transformationsright chevron icon

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Q. What kind of transformation converts the graph of f(x)=4∣x−8∣+8f(x) = 4|x - 8| + 8 into the graph of g(x)=4∣x−8∣−1g(x) = 4|x - 8| - 1?\newlineChoices:\newline(A) translation 99 units down\newline(B) translation 99 units up\newline(C) translation 99 units right\newline(D) translation 99 units left
  1. Identify Vertex: Identify the vertex of the function f(x)=4∣x−8∣+8f(x) = 4|x - 8| + 8.\newlineVertex of f(x)f(x): (8,8)(8, 8)
  2. Calculate Difference: Identify the vertex of the function g(x)=4∣x−8∣−1g(x) = 4|x - 8| - 1.\newlineVertex of g(x)g(x): (8,−1)(8, -1)
  3. Determine Transformation: Calculate the difference between the y-coordinates of the vertices of f(x)f(x) and g(x)g(x).\newlineDifference: 8−(−1)=98 - (-1) = 9
  4. Determine Transformation: Calculate the difference between the y-coordinates of the vertices of f(x)f(x) and g(x)g(x).\newlineDifference: 8−(−1)=98 - (-1) = 9 Determine the direction of the transformation based on the difference in y-coordinates.\newlineSince the y-coordinate of g(x)g(x) is 99 units less than the y-coordinate of f(x)f(x), the transformation is a translation 99 units down.

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