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What kind of transformation converts the graph of f(x)=−3∣x−4∣+5f(x) = -3|x - 4| + 5 into the graph of g(x)=−3∣x−7∣+5g(x) = -3|x - 7| + 5?\newlineChoices:\newline(A) translation 33 units right\newline(B) translation 33 units left\newline(C) translation 33 units up\newline(D) translation 33 units down

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Q. What kind of transformation converts the graph of f(x)=−3∣x−4∣+5f(x) = -3|x - 4| + 5 into the graph of g(x)=−3∣x−7∣+5g(x) = -3|x - 7| + 5?\newlineChoices:\newline(A) translation 33 units right\newline(B) translation 33 units left\newline(C) translation 33 units up\newline(D) translation 33 units down
  1. Find Vertex of f(x)f(x): Find the vertex of f(x)=−3∣x−4∣+5f(x) = -3|x - 4| + 5.\newlineVertex of f(x)f(x) is at x=4x = 4, y=5y = 5.
  2. Find Vertex of g(x)g(x): Find the vertex of g(x)=−3∣x−7∣+5g(x) = -3|x - 7| + 5.\newlineVertex of g(x)g(x) is at x=7x = 7, y=5y = 5.
  3. Calculate Horizontal Shift: Calculate the horizontal shift between the vertices of f(x)f(x) and g(x)g(x).Shift=7−4=3\text{Shift} = 7 - 4 = 3 units to the right.

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