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What kind of transformation converts the graph of f(x)=−10(x+10)2−9f(x) = -10(x + 10)^2 - 9 into the graph of g(x)=−10(x+10)2−8g(x) = -10(x + 10)^2 - 8?\newlineChoices:\newline(A) translation 11 unit down\newline(B) translation 11 unit right\newline(C) translation 11 unit left\newline(D) translation 11 unit up

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Q. What kind of transformation converts the graph of f(x)=−10(x+10)2−9f(x) = -10(x + 10)^2 - 9 into the graph of g(x)=−10(x+10)2−8g(x) = -10(x + 10)^2 - 8?\newlineChoices:\newline(A) translation 11 unit down\newline(B) translation 11 unit right\newline(C) translation 11 unit left\newline(D) translation 11 unit up
  1. Analyze Functions: Analyze the given functions to determine the type of transformation.\newlineThe given functions are f(x)=−10(x+10)2−9f(x) = -10(x + 10)^2 - 9 and g(x)=−10(x+10)2−8g(x) = -10(x + 10)^2 - 8. We need to compare these two functions to understand how g(x)g(x) is obtained from f(x)f(x).
  2. Compare Y-Values: Compare the y-values of the functions.\newlineThe only difference between f(x)f(x) and g(x)g(x) is the constant term at the end of the equation. f(x)f(x) has a constant term of −9-9, while g(x)g(x) has a constant term of −8-8.
  3. Determine Shift Direction: Determine the direction of the shift.\newlineSince the constant term in g(x)g(x) is one unit greater than the constant term in f(x)f(x), this indicates a vertical shift upwards by 11 unit.
  4. Match Transformation: Match the transformation with the given choices.\newlineThe transformation is a vertical shift, so it cannot be a translation to the left or right. Between the two remaining choices, translation 11 unit down or translation 11 unit up, we have determined that the shift is upwards. Therefore, the correct choice is translation 11 unit up.

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