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What kind of transformation converts the graph of f(x)=−7∣x+5∣−8f(x) = -7|x + 5| - 8 into the graph of g(x)=−7∣x+5∣−10g(x) = -7|x + 5| - 10?\newlineChoices:\newline(A) translation 22 units up\newline(B) translation 22 units right\newline(C) translation 22 units left\newline(D) translation 22 units down

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Describe function transformationsright chevron icon

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Q. What kind of transformation converts the graph of f(x)=−7∣x+5∣−8f(x) = -7|x + 5| - 8 into the graph of g(x)=−7∣x+5∣−10g(x) = -7|x + 5| - 10?\newlineChoices:\newline(A) translation 22 units up\newline(B) translation 22 units right\newline(C) translation 22 units left\newline(D) translation 22 units down
  1. Analyze Functions: Analyze the given functions.\newlineWe have f(x)=−7∣x+5∣−8f(x) = -7|x + 5| - 8 and g(x)=−7∣x+5∣−10g(x) = -7|x + 5| - 10. Compare the two functions to determine the type of transformation.
  2. Identify Difference: 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 −8-8, and g(x)g(x) has −10-10.
  3. Determine Transformation: Determine the direction of the transformation.\newlineSince the change is in the constant term, and it is a decrease from −8-8 to −10-10, this indicates a vertical shift.
  4. Calculate Magnitude: Calculate the magnitude of the transformation.\newlineThe change from −8-8 to −10-10 is a decrease of 22 units. This means the graph has moved down by 22 units.
  5. Conclude Transformation: Conclude the type of transformation.\newlineThe graph of f(x)f(x) has been translated 22 units down to become the graph of g(x)g(x).

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