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What kind of transformation converts the graph of f(x)=6∣x+1∣+8f(x) = 6|x + 1| + 8 into the graph of g(x)=6∣x+1∣−1g(x) = 6|x + 1| - 1?\newlineChoices:\newline(A) translation 99 units left\newline(B) translation 99 units up\newline(C) translation 99 units right\newline(D) translation 99 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+1∣+8f(x) = 6|x + 1| + 8 into the graph of g(x)=6∣x+1∣−1g(x) = 6|x + 1| - 1?\newlineChoices:\newline(A) translation 99 units left\newline(B) translation 99 units up\newline(C) translation 99 units right\newline(D) translation 99 units down
  1. Identify Basic Form: Identify the basic form of the functions and the transformation involved.\newlineThe function f(x)=6∣x+1∣+8f(x) = 6|x + 1| + 8 is a vertical translation of the parent function 6∣x∣6|x| by 88 units up and 11 unit left. The function g(x)=6∣x+1∣−1g(x) = 6|x + 1| - 1 is also a vertical translation of the parent function 6∣x∣6|x| but with a different vertical shift.
  2. Determine Vertical Shift: Determine the vertical shift between the two functions. The vertical shift can be found by comparing the constant terms of f(x)f(x) and g(x)g(x). The constant term in f(x)f(x) is +8+8, and the constant term in g(x)g(x) is −1-1.
  3. Calculate Shift Difference: Calculate the difference in the vertical shift.\newlineThe difference in the vertical shift is −1−(+8)=−9-1 - (+8) = -9. This means that the graph of g(x)g(x) is shifted 99 units down from the graph of f(x)f(x).

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