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What kind of transformation converts the graph of f(x)=5∣x+10∣−6f(x) = 5|x + 10| - 6 into the graph of g(x)=5∣x+5∣−6g(x) = 5|x + 5| - 6?\newlineChoices:\newline(A) translation 55 units down\newline(B) translation 55 units up\newline(C) translation 55 units left\newline(D) translation 55 units right

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Q. What kind of transformation converts the graph of f(x)=5∣x+10∣−6f(x) = 5|x + 10| - 6 into the graph of g(x)=5∣x+5∣−6g(x) = 5|x + 5| - 6?\newlineChoices:\newline(A) translation 55 units down\newline(B) translation 55 units up\newline(C) translation 55 units left\newline(D) translation 55 units right
  1. Identify Transformation: Identify the transformation affecting the absolute value expression.\newlineThe absolute value function f(x)=5∣x+10∣−6f(x) = 5|x + 10| - 6 has been changed to g(x)=5∣x+5∣−6g(x) = 5|x + 5| - 6. The change is inside the absolute value from ∣x+10∣|x + 10| to ∣x+5∣|x + 5|. This suggests a horizontal shift.
  2. Determine Shift Direction: Determine the direction and magnitude of the horizontal shift. The expression inside the absolute value has changed from (x+10)(x + 10) to (x+5)(x + 5). This indicates a shift to the left by 55 units because the value added to xx has decreased by 55.
  3. Match Transformation to Choices: Match the transformation to the given choices.\newlineThe transformation is a horizontal shift to the left by 55 units. This corresponds to choice (C) translation 55 units left.

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