What kind of transformation converts the graph of f(x) = -2|x - 4| - 2 into the graph of g(x) = -2|x - 4| - 6? Choices: (A)translation 4 units right (B)translation 4 units up (C)translation 4 units left (D)translation 4 units down

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What kind of transformation converts the graph of f(x) = -2|x - 4| - 2 into the graph of g(x) = -2|x - 4| - 6?   Choices: (A)translation 4 units right (B)translation 4 units up (C)translation 4 units left (D)translation 4 units down

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Identify Vertex of f(x): Identify the vertex of the function f(x) = -2|x - 4| - 2. The vertex of the absolute value function f(x) = -2|x - 4| - 2 is at the point where the expression inside the absolute value is zero, which is at x = 4. The y-coordinate of the vertex is the value of the function when x = 4, which is f(4) = -2|4 - 4| - 2 = -2. So, the vertex of f(x) is (4, -2).Identify Vertex of g(x): Identify the vertex of the function g(x) = -2|x - 4| - 6. Similarly, the vertex of the absolute value function g(x) = -2|x - 4| - 6 is at the point where the expression inside the absolute value is zero, which is at x = 4. The y-coordinate of the vertex is the value of the function when x = 4, which is g(4) = -2|4 - 4| - 6 = -6. So, the vertex of g(x) is (4, -6).Determine Transformation: Determine the transformation from f(x) to g(x). The x-coordinates of the vertices of f(x) and g(x) are the same, so there is no horizontal shift. The y-coordinate of the vertex of g(x) is 4 units lower than the y-coordinate of the vertex of f(x) (-6 compared to -2). This indicates a vertical shift. The transformation is a translation 4 units down.

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