What kind of transformation converts the graph of f(x) = 8|x - 5| + 5 into the graph of g(x) = 8|x - 5| + 10? Choices: (A)translation 5 units up (B)translation 5 units left (C)translation 5 units down (D)translation 5 units right

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What kind of transformation converts the graph of f(x) = 8|x - 5| + 5 into the graph of g(x) = 8|x - 5| + 10?   Choices: (A)translation 5 units up (B)translation 5 units left (C)translation 5 units down (D)translation 5 units right

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Identify Vertex: Identify the vertex of the function f(x) = 8|x - 5| + 5. The vertex of the absolute value function f(x) = 8|x - 5| + 5 is at the point where the expression inside the absolute value is zero, which is at x = 5. The y-coordinate of the vertex is the constant term outside the absolute value, which is +5. Therefore, the vertex of f(x) is (5, 5).Identify Vertex: Identify the vertex of the function g(x) = 8|x - 5| + 10. Similarly, the vertex of the absolute value function g(x) = 8|x - 5| + 10 is at the point where the expression inside the absolute value is zero, which is at x = 5. The y-coordinate of the vertex is the constant term outside the absolute value, which is +10. Therefore, the vertex of g(x) is (5, 10).Determine Transformation: Determine the transformation from f(x) to g(x). Comparing the vertices of f(x) and g(x), we see that the x-coordinate remains the same (5), but the y-coordinate has increased from 5 to 10. This indicates a vertical shift. The change in the y-coordinate is from 5 to 10, which is an increase of 5 units.Identify Transformation Type: Identify the type of transformation based on the change in the y-coordinate. Since the y-coordinate of the vertex has increased by 5 units, the transformation is a translation 5 units up.

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