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What kind of transformation converts the graph of f(x)=6∣x−7∣−2f(x) = 6|x - 7| - 2 into the graph of g(x)=6∣x−7∣+1g(x) = 6|x - 7| + 1?\newlineChoices:\newline(A) translation 33 units left\newline(B) translation 33 units right\newline(C) translation 33 units up\newline(D) translation 33 units down

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Describe function transformationsright chevron icon

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Q. What kind of transformation converts the graph of f(x)=6∣x−7∣−2f(x) = 6|x - 7| - 2 into the graph of g(x)=6∣x−7∣+1g(x) = 6|x - 7| + 1?\newlineChoices:\newline(A) translation 33 units left\newline(B) translation 33 units right\newline(C) translation 33 units up\newline(D) translation 33 units down
  1. Identify Function Forms: Identify the basic form of the functions and the transformation involved.\newlineThe function f(x)=6∣x−7∣−2f(x) = 6|x - 7| - 2 is an absolute value function with a vertex at (7,−2)(7, -2). The function g(x)=6∣x−7∣+1g(x) = 6|x - 7| + 1 is also an absolute value function with the same slope and opening direction, but with a different y-intercept.
  2. Determine Vertical Shift: Determine the vertical shift between the two functions.\newlineThe only difference between f(x)f(x) and g(x)g(x) is the constant term at the end of the equation. The constant term in f(x)f(x) is −2-2, and in g(x)g(x) it is +1+1. To go from −2-2 to +1+1, you need to add 33.
  3. Identify Transformation Type: Identify the type of transformation based on the change in the constant term. Adding 33 to the constant term corresponds to a vertical shift upwards by 33 units.
  4. Match Transformation to Choices: Match the transformation to the given choices.\newlineThe transformation that converts f(x)f(x) to g(x)g(x) is a translation 33 units up, which matches choice (C).

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