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What kind of transformation converts the graph of f(x)=10(x−1)2+1f(x) = 10(x - 1)^2 + 1 into the graph of g(x)=10(x−1)2g(x) = 10(x - 1)^2?\newlineChoices:\newline(A) translation 11 unit up\newline(B) translation 11 unit down\newline(C) translation 11 unit right\newline(D) translation 11 unit left

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Q. What kind of transformation converts the graph of f(x)=10(x−1)2+1f(x) = 10(x - 1)^2 + 1 into the graph of g(x)=10(x−1)2g(x) = 10(x - 1)^2?\newlineChoices:\newline(A) translation 11 unit up\newline(B) translation 11 unit down\newline(C) translation 11 unit right\newline(D) translation 11 unit left
  1. Compare functions: Compare f(x)f(x) and g(x)g(x) to see the difference.f(x)=10(x−1)2+1f(x) = 10(x - 1)^2 + 1g(x)=10(x−1)2g(x) = 10(x - 1)^2The only difference is the +1+1 at the end of f(x)f(x).
  2. Determine transformation type: Determine the type of transformation.\newlineThe ＂+1＂＂+1＂ in f(x)f(x) affects the yy-value of the graph, so it's a vertical shift.
  3. Find shift direction: Figure out the direction of the shift.\newlineSince g(x)g(x) doesn't have the ＂+1＂＂+1＂, the graph of f(x)f(x) has been shifted down by 11 unit to get g(x)g(x).
  4. Identify correct choice: Identify the correct choice.\newlineThe graph of f(x)f(x) is shifted down by 11 unit to become g(x)g(x).\newlineSo, the transformation is a translation 11 unit down.

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