Final answer:
The correct absolute value equation that reflects over the x-axis, vertically compresses by a factor of 1/3, and translates 6 to the right is |x-6|/3. However, none of the provided options include the vertical compression, so the closest option is (b) |x-6|.
Step-by-step explanation:
The question involves transforming an absolute value function based on given geometric transformations. Reflecting a graph over the x-axis can be achieved by multiplying the function by -1. A vertical compression by a factor of 1/3 means we have to multiply the function by 1/3. Translating the graph 6 units to the right involves replacing x with (x-6). Therefore, combining these transformations, the correct absolute value equation is |x-6|/3, reflecting the function over the x-axis, vertically compressing it, and shifting it to the right.
However, all of the provided options lack the vertical compression factor. The option closest to representing the correct transformations is (b) |x-6|, which reflects the function over the x-axis and translates it 6 units to the right, but does not compress it vertically.