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What kind of transformation converts the graph of f(x)=−10(x−5)2−1f(x) = -10(x - 5)^2 - 1 into the graph of g(x)=−10(x−5)2−10g(x) = -10(x - 5)^2 - 10?\newlineChoices:\newline(A) translation 99 units up\newline(B) translation 99 units right\newline(C) translation 99 units left\newline(D) translation 99 units down

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Q. What kind of transformation converts the graph of f(x)=−10(x−5)2−1f(x) = -10(x - 5)^2 - 1 into the graph of g(x)=−10(x−5)2−10g(x) = -10(x - 5)^2 - 10?\newlineChoices:\newline(A) translation 99 units up\newline(B) translation 99 units right\newline(C) translation 99 units left\newline(D) translation 99 units down
  1. Compare Functions: Compare the two functions f(x)f(x) and g(x)g(x).f(x)=−10(x−5)2−1f(x) = -10(x - 5)^2 - 1g(x)=−10(x−5)2−10g(x) = -10(x - 5)^2 - 10Notice that the only difference is the constant term at the end.
  2. Determine Change: Determine the change in the constant term.\newlineThe constant term in f(x)f(x) is −1-1 and in g(x)g(x) it is −10-10.\newlineCalculate the difference: −10−(−1)=−10+1=−9-10 - (-1) = -10 + 1 = -9.
  3. Identify Shift Direction: Identify the direction of the shift. Since the constant term decreased by 99, the graph shifts down by 99 units.
  4. Match Transformation: Match the transformation with the given choices.\newlineThe graph shifts 99 units down, so the correct choice is (D) translation 99 units down.

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