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Answer :
The function is best represented by g(x) = |x - 2| - 4, exhibiting a shift of the absolute value function two units to the right and four units downward.
Let's analyze the given points on the graph:
1. Starting from (6,0) to (-4,-2), the graph moves from right to left and slightly downward.
2. Then from (-4,-2) to (-2,0), it moves slightly upward and to the left.
3. From (-2,0) to (0,2), it moves straight upward.
4. Finally, from (0,2) to (4,6), it moves upward and to the right.
Considering the shape of the graph and the direction it moves between the given points, the absolute value function g(x) = |x - 2| - 4 best represents it. This function represents a shift of the absolute value function |x| two units to the right and four units downward. Therefore, the correct equation is:
[tex]\[ g(x) = |x - 2| - 4 \][/tex]
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