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What kind of transformation converts the graph of f(x)=−∣x+9∣+7f(x) = -|x + 9| + 7 into the graph of g(x)=−∣x+9∣+10g(x) = -|x + 9| + 10?\newlineChoices:\newline(A) translation 33 units up\newline(B) translation 33 units right\newline(C) translation 33 units left\newline(D) translation 33 units down

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Q. What kind of transformation converts the graph of f(x)=−∣x+9∣+7f(x) = -|x + 9| + 7 into the graph of g(x)=−∣x+9∣+10g(x) = -|x + 9| + 10?\newlineChoices:\newline(A) translation 33 units up\newline(B) translation 33 units right\newline(C) translation 33 units left\newline(D) translation 33 units down
  1. Analyze functions f(x)f(x) and g(x)g(x): Analyze the given functions f(x)f(x) and g(x)g(x).f(x)=−∣x+9∣+7f(x) = -|x + 9| + 7g(x)=−∣x+9∣+10g(x) = -|x + 9| + 10Compare the two functions to determine the type of transformation.
  2. Identify differences in functions: Identify the change in the functions.\newlineThe only difference between f(x)f(x) and g(x)g(x) is the constant term at the end of the equation. f(x)f(x) has +7+7, while g(x)g(x) has +10+10.
  3. Determine direction of transformation: Determine the direction of the transformation. Since the change is in the constant term, and it is an increase from +7+7 to +10+10, this indicates a vertical shift.
  4. Calculate magnitude of transformation: Calculate the magnitude of the transformation.\newlineThe change in the constant term is from +7+7 to +10+10, which is an increase of 33 units.
  5. Conclude type of transformation: Conclude the type of transformation.\newlineThe graph of f(x)f(x) is shifted vertically upwards by 33 units to obtain the graph of g(x)g(x).

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