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What kind of transformation converts the graph of f(x)=−10∣x−8∣−10f(x) = -10|x - 8| - 10 into the graph of g(x)=−10∣x−8∣−7g(x) = -10|x - 8| - 7?\newlineChoices:\newline(A) translation 33 units up\newline(B) translation 33 units left\newline(C) translation 33 units down\newline(D) translation 33 units right

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Describe function transformationsright chevron icon

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Q. What kind of transformation converts the graph of f(x)=−10∣x−8∣−10f(x) = -10|x - 8| - 10 into the graph of g(x)=−10∣x−8∣−7g(x) = -10|x - 8| - 7?\newlineChoices:\newline(A) translation 33 units up\newline(B) translation 33 units left\newline(C) translation 33 units down\newline(D) translation 33 units right
  1. Analyze Functions: Analyze the given functions to determine the type of transformation.\newlineWe have f(x)=−10∣x−8∣−10f(x) = -10|x - 8| - 10 and g(x)=−10∣x−8∣−7g(x) = -10|x - 8| - 7. The only difference between f(x)f(x) and g(x)g(x) is the constant term at the end of the equation. This indicates a vertical shift.
  2. Vertical Shift Direction: Determine the direction of the vertical shift. The constant term in f(x)f(x) is −10-10, and in g(x)g(x) it is −7-7. Since −7-7 is greater than −10-10, the graph of g(x)g(x) is shifted up compared to the graph of f(x)f(x).
  3. Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. The difference between the constant terms is −7−(−10)=3-7 - (-10) = 3. This means the graph of g(x)g(x) is shifted 33 units up from the graph of f(x)f(x).

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