What kind of transformation converts the graph of f(x) = 2|x - 5| + 1 into the graph of g(x) = 2|x + 5| + 1? Choices: (A)translation 10 units down (B)translation 10 units up (C)translation 10 units left (D)translation 10 units right

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What kind of transformation converts the graph of f(x) = 2|x - 5| + 1 into the graph of g(x) = 2|x + 5| + 1?   Choices: (A)translation 10 units down (B)translation 10 units up (C)translation 10 units left (D)translation 10 units right

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Identify Vertex of f(x): Identify the vertex of the function f(x) = 2|x - 5| + 1. The vertex of the absolute value function f(x) = 2|x - 5| + 1 is at the point where the expression inside the absolute value is zero. This occurs at x = 5. The y-coordinate of the vertex is the value of the function when x = 5, which is f(5) = 2|5 - 5| + 1 = 2|0| + 1 = 2(0) + 1 = 1. Therefore, the vertex of f(x) is (5, 1).Identify Vertex of g(x): Identify the vertex of the function g(x) = 2|x + 5| + 1. Similarly, the vertex of the absolute value function g(x) = 2|x + 5| + 1 is at the point where the expression inside the absolute value is zero. This occurs at x = -5. The y-coordinate of the vertex is the value of the function when x = -5, which is g(-5) = 2|-5 + 5| + 1 = 2|0| + 1 = 2(0) + 1 = 1. Therefore, the vertex of g(x) is (-5, 1).Determine Transformation Type: Determine the type of transformation from f(x) to g(x). The vertex of f(x) is (5, 1) and the vertex of g(x) is (-5, 1). The transformation from f(x) to g(x) involves a horizontal shift, since the y-coordinates of the vertices are the same, but the x-coordinates are different. The shift is from x = 5 to x = -5, which is a shift of 10 units to the left.

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