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What kind of transformation converts the graph of f(x)=2∣x−10∣f(x) = 2|x - 10| into the graph of g(x)=2∣x−10∣−3g(x) = 2|x - 10| - 3?\newlineChoices:\newline(A) translation 33 units up\newline(B) translation 33 units down\newline(C) translation 33 units left\newline(D) translation 33 units right

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Q. What kind of transformation converts the graph of f(x)=2∣x−10∣f(x) = 2|x - 10| into the graph of g(x)=2∣x−10∣−3g(x) = 2|x - 10| - 3?\newlineChoices:\newline(A) translation 33 units up\newline(B) translation 33 units down\newline(C) translation 33 units left\newline(D) translation 33 units right
  1. Compare Functions: To determine the type of transformation from f(x)f(x) to g(x)g(x), we need to compare the two functions and see how they differ. The function f(x)=2∣x−10∣f(x) = 2|x - 10| is being transformed into g(x)=2∣x−10∣−3g(x) = 2|x - 10| - 3. We can see that the only difference between f(x)f(x) and g(x)g(x) is the subtraction of 33 from the entire function.
  2. Identify Difference: Since the subtraction of 33 affects the entire function, it means that every yy-value of the graph of f(x)f(x) is decreased by 33 to get the corresponding yy-value of the graph of g(x)g(x). This is a vertical shift.
  3. Vertical Shift Down: A vertical shift down by 33 units is represented by subtracting 33 from the function. Therefore, the transformation that converts f(x)f(x) into g(x)g(x) is a translation 33 units down.

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