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

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Q. What kind of transformation converts the graph of f(x)=−5∣x−10∣−5f(x) = -5|x - 10| - 5 into the graph of g(x)=−5∣x−10∣+5g(x) = -5|x - 10| + 5?\newlineChoices:\newline(A) translation 1010 units left\newline(B) translation 1010 units up\newline(C) translation 1010 units right\newline(D) translation 1010 units down
  1. Identify Change: Identify the change between f(x)f(x) and g(x)g(x).f(x)=−5∣x−10∣−5f(x) = -5|x - 10| - 5g(x)=−5∣x−10∣+5g(x) = -5|x - 10| + 5The only change is in the constant term at the end of the equation.
  2. Direction of Shift: Determine the direction of the shift.\newlineThe constant term in f(x)f(x) is −5-5, and in g(x)g(x) it is +5+5.\newlineThis indicates a vertical shift, not horizontal.
  3. Magnitude Calculation: Calculate the magnitude of the shift.\newlineThe change in the constant term is from −5-5 to +5+5, which is a change of 1010 units.
  4. Shift Direction: Determine if the shift is upwards or downwards.\newlineSince the constant term increased from −5-5 to +5+5, the graph shifts upwards.
  5. Match Transformation: Match the transformation with the given choices.\newlineThe graph shifts 1010 units up, which corresponds to choice (B)(B).

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