Final answer:
To identify the equation representing the function graphed on the coordinate plane, one should analyze the vertex and shifts from the parent function's position to determine the correct translation and reflection properties of the absolute value function.
Step-by-step explanation:
The equation representing a function graphed on the coordinate plane is determined based on the specific features of the graph such as vertex, direction of the opening, and translations from the origin. A function of the form g(x) = |x - h| + k represents a vertical translation by k units and a horizontal translation by h units of the parent function f(x) = |x|. The graph of g(x) = |x + 4| – 2 would be translated 4 units to the left and 2 units down, while g(x) = |x – 4| – 2 would be translated 4 units to the right and 2 units down, and so on for the respective translations indicated by each function's equation.
Without the actual graph provided for direct analysis, an accurate determination of the correct equation cannot be made. However, when given the graph of an absolute value function, one should look for the vertex (the point where the graph changes direction) and any vertical or horizontal shifts from the standard position to correctly identify the equation that represents the function graphed on the coordinate plane.