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What kind of transformation converts the graph of f(x)=7∣x−6∣f(x) = 7|x - 6| into the graph of g(x)=7∣x∣g(x) = 7|x|?\newlineChoices:\newline(A) translation 66 units right\newline(B) translation 66 units down\newline(C) translation 66 units up\newline(D) translation 66 units left

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Q. What kind of transformation converts the graph of f(x)=7∣x−6∣f(x) = 7|x - 6| into the graph of g(x)=7∣x∣g(x) = 7|x|?\newlineChoices:\newline(A) translation 66 units right\newline(B) translation 66 units down\newline(C) translation 66 units up\newline(D) translation 66 units left
  1. Identify Shape of f(x)f(x): Identify the basic shape of the function f(x)=7∣x−6∣f(x) = 7|x - 6|.\newlineThe function f(x)=7∣x−6∣f(x) = 7|x - 6| is an absolute value function with a vertex at (6,0)(6, 0) because the expression inside the absolute value is x−6x - 6, which is zero when x=6x = 6.
  2. Identify Shape of g(x)g(x): Identify the basic shape of the function g(x)=7∣x∣g(x) = 7|x|.\newlineThe function g(x)=7∣x∣g(x) = 7|x| is also an absolute value function with a vertex at (0,0)(0, 0) because the expression inside the absolute value is xx, which is zero when x=0x = 0.
  3. Determine Transformation: Determine the transformation required to go from f(x)f(x) to g(x)g(x). To go from f(x)=7∣x−6∣f(x) = 7|x - 6| to g(x)=7∣x∣g(x) = 7|x|, we need to move the vertex of the graph from (6,0)(6, 0) to (0,0)(0, 0). This is a horizontal shift to the left by 66 units.

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