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What kind of transformation converts the graph of f(x)=−6∣x+5∣+4f(x) = -6|x + 5| + 4 into the graph of g(x)=−6∣x+5∣+10g(x) = -6|x + 5| + 10?\newlineChoices:\newline(A) translation 66 units left\newline(B) translation 66 units down\newline(C) translation 66 units right\newline(D) translation 66 units up

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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+5∣+4f(x) = -6|x + 5| + 4 into the graph of g(x)=−6∣x+5∣+10g(x) = -6|x + 5| + 10?\newlineChoices:\newline(A) translation 66 units left\newline(B) translation 66 units down\newline(C) translation 66 units right\newline(D) translation 66 units up
  1. Compare Functions: Compare the two functions f(x)f(x) and g(x)g(x) to determine the transformation.f(x)=−6∣x+5∣+4f(x) = -6|x + 5| + 4g(x)=−6∣x+5∣+10g(x) = -6|x + 5| + 10The only difference is the constant term at the end of the function.
  2. Identify Change: Identify the change in the constant term from f(x)f(x) to g(x)g(x). The constant term in f(x)f(x) is +4+4, and in g(x)g(x) it's +10+10.
  3. Calculate Difference: Calculate the difference in the constant terms to find the vertical shift.\newlineDifference = 10−4=610 - 4 = 6\newlineThis indicates a vertical shift of 66 units.
  4. Determine Shift Direction: Determine the direction of the vertical shift.\newlineSince the constant term increased from 44 to 1010, the graph shifts up.

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