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What kind of transformation converts the graph of f(x)=−4(x+8)2−9f(x) = -4(x + 8)^2 - 9 into the graph of g(x)=−4(x+8)2−7g(x) = -4(x + 8)^2 - 7?\newlineChoices:\newline(A) translation 22 units down\newline(B) translation 22 units left\newline(C) translation 22 units right\newline(D) translation 22 units up

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Q. What kind of transformation converts the graph of f(x)=−4(x+8)2−9f(x) = -4(x + 8)^2 - 9 into the graph of g(x)=−4(x+8)2−7g(x) = -4(x + 8)^2 - 7?\newlineChoices:\newline(A) translation 22 units down\newline(B) translation 22 units left\newline(C) translation 22 units right\newline(D) translation 22 units up
  1. Analyze Functions: Analyze the given functions.\newlineWe have f(x)=−4(x+8)2−9f(x) = -4(x + 8)^2 - 9 and g(x)=−4(x+8)2−7g(x) = -4(x + 8)^2 - 7. Compare the two functions to determine the type of transformation.
  2. Identify Change: Identify the change in 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 −9-9, and g(x)g(x) has −7-7.
  3. Determine Transformation Direction: Determine the direction of the transformation.\newlineSince the change is in the constant term, and it is from −9-9 to −7-7, this indicates a vertical shift. The graph is moving up because the yy-value at every xx is increasing by 22.
  4. Calculate Transformation Magnitude: Calculate the magnitude of the transformation.\newlineThe change in the constant term is from −9-9 to −7-7, which is an increase of 22 units. Therefore, the graph of f(x)f(x) is translated 22 units up to become g(x)g(x).

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