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What kind of transformation converts the graph of f(x)=10∣x−8∣+4f(x) = 10|x - 8| + 4 into the graph of g(x)=10∣x−8∣+9g(x) = 10|x - 8| + 9?\newlineChoices:\newline(A) translation 55 units left\newline(B) translation 55 units right\newline(C) translation 55 units down\newline(D) translation 55 units up

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Q. What kind of transformation converts the graph of f(x)=10∣x−8∣+4f(x) = 10|x - 8| + 4 into the graph of g(x)=10∣x−8∣+9g(x) = 10|x - 8| + 9?\newlineChoices:\newline(A) translation 55 units left\newline(B) translation 55 units right\newline(C) translation 55 units down\newline(D) translation 55 units up
  1. Identify Vertex f(x)f(x): Identify the vertex of the function f(x)=10∣x−8∣+4f(x) = 10|x - 8| + 4.\newlineVertex of f(x)f(x): (8,4)(8, 4)
  2. Identify Vertex g(x)g(x): Identify the vertex of the function g(x)=10∣x−8∣+9g(x) = 10|x - 8| + 9.\newlineVertex of g(x)g(x): (8,9)(8, 9)
  3. Calculate Y-Coordinate Difference: Calculate the difference between the y-coordinates of the vertices of f(x)f(x) and g(x)g(x).\newlineDifference in y-coordinates: 9−4=59 - 4 = 5
  4. Determine Translation Direction: Determine the direction of the translation based on the difference in yy-coordinates.\newlineSince the yy-coordinate increased by 55, the graph has been translated 55 units up.

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