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What kind of transformation converts the graph of f(x)=−10∣x−1∣+1f(x) = -10|x - 1| + 1 into the graph of g(x)=−10∣x−10∣+1g(x) = -10|x - 10| + 1?\newlineChoices:\newline(A) translation 99 units right\newline(B) translation 99 units up\newline(C) translation 99 units down\newline(D) translation 99 units left

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Q. What kind of transformation converts the graph of f(x)=−10∣x−1∣+1f(x) = -10|x - 1| + 1 into the graph of g(x)=−10∣x−10∣+1g(x) = -10|x - 10| + 1?\newlineChoices:\newline(A) translation 99 units right\newline(B) translation 99 units up\newline(C) translation 99 units down\newline(D) translation 99 units left
  1. Find Vertex of f(x)f(x): Find the vertex of f(x)f(x).f(x)=−10∣x−1∣+1f(x) = -10|x - 1| + 1 has a vertex at (1,1)(1, 1).
  2. Find Vertex of g(x)g(x): Find the vertex of g(x)g(x).g(x)=−10∣x−10∣+1g(x) = -10|x - 10| + 1 has a vertex at (10,1)(10, 1).
  3. Compare Vertex x-coordinates: Compare the x-coordinates of the vertices of f(x)f(x) and g(x)g(x). The x-coordinate of f(x)f(x) is 11 and the x-coordinate of g(x)g(x) is 1010.
  4. Determine Shift Direction: Determine the direction of the shift. The xx-coordinate increased from 11 to 1010, so the graph shifted to the right.
  5. Calculate Shift Amount: Calculate the amount of the shift. 10−1=910 - 1 = 9 The graph shifted 99 units to the right.

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