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What kind of transformation converts the graph of f(x)=3∣x+4∣f(x) = 3|x + 4| into the graph of g(x)=3∣x+4∣−5g(x) = 3|x + 4| - 5?\newlineChoices:\newline(A) translation 55 units down\newline(B) translation 55 units up\newline(C) translation 55 units right\newline(D) translation 55 units left

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Q. What kind of transformation converts the graph of f(x)=3∣x+4∣f(x) = 3|x + 4| into the graph of g(x)=3∣x+4∣−5g(x) = 3|x + 4| - 5?\newlineChoices:\newline(A) translation 55 units down\newline(B) translation 55 units up\newline(C) translation 55 units right\newline(D) translation 55 units left
  1. Identify Function and Transformation: Identify the basic function and the transformation applied.\newlineThe basic function is f(x)=3∣x+4∣f(x) = 3|x + 4|. The transformation applied to f(x)f(x) to obtain g(x)g(x) is a vertical shift, as indicated by the −5- 5 at the end of g(x)=3∣x+4∣−5g(x) = 3|x + 4| - 5.
  2. Vertical Shift Direction: Determine the direction of the vertical shift.\newlineSince the transformation involves subtracting 55 from the entire function, this indicates a downward shift of the graph by 55 units.
  3. Match Transformation to Choices: Match the transformation to the given choices.\newlineThe transformation is a vertical shift downward by 55 units, which corresponds to choice (A) translation 55 units down.

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