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Which equation represents g(x)? The graph of g(x) is a reflection and translation of f(x) = x.

A. g(x) = 3x + 1
B. g(x) = 3/-1
C. g(x) = -3x + 1

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Final answer:

The equation that represents g(x) as a reflection and translation of f(x) = x is g(x) = -3x + 1, which reflects a negative slope and a translated y-intercept.

Step-by-step explanation:

The goal is to determine which equation represents the function g(x) given that it is a reflection and translation of f(x) = x. Reflection over the x-axis inverts the sign of the slope in the linear function, and translation involves shifting the graph vertically or horizontally.

The original function f(x) = x has a slope of 1 and no y-intercept term (which can be thought of as 0). Therefore, a reflection over the x-axis would change the slope to -1. If there is a translation, it means we should expect a change in the y-intercept (b term). A candidate function for g(x) would be g(x) = -x + b, where b is the y-intercept after translation.

Looking at the provided options, g(x) = -3x + 1 is the one that represents a reflection of the slope of f(x) since the slope has changed from positive to negative, and it also includes a translation by an increase of 1 in the y-intercept.

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