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What kind of transformation converts the graph of f(x)=5∣x−1∣f(x) = 5|x - 1| into the graph of g(x)=5∣x−1∣−10g(x) = 5|x - 1| - 10?\newlineChoices:\newline(A) translation 1010 units up\newline(B) translation 1010 units down\newline(C) translation 1010 units left\newline(D) translation 1010 units right

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Q. What kind of transformation converts the graph of f(x)=5∣x−1∣f(x) = 5|x - 1| into the graph of g(x)=5∣x−1∣−10g(x) = 5|x - 1| - 10?\newlineChoices:\newline(A) translation 1010 units up\newline(B) translation 1010 units down\newline(C) translation 1010 units left\newline(D) translation 1010 units right
  1. Identify Function: Identify the basic function and its transformation.\newlineThe basic function here is f(x)=5∣x−1∣f(x) = 5|x - 1|. The transformation applied to f(x)f(x) to obtain g(x)g(x) is a vertical shift, as indicated by the −10- 10 added to the function.
  2. Direction of Shift: Determine the direction of the vertical shift.\newlineSince −10- 10 is subtracted from the basic function, this indicates a downward shift of the graph.
  3. Magnitude of Shift: Determine the magnitude of the vertical shift. The magnitude of the shift is the absolute value of the number subtracted from the basic function, which is 1010 units.
  4. Conclusion: Conclude the type of transformation.\newlineThe transformation is a translation 1010 units down, which matches choice (B)(B).

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