To find the equation for the function represented by the graph, we need to determine the transformation that was applied to the graph of the square root function.
From the given points, we can see that the point (1, 2) on the original square root function has been transformed to the point (2, -1) on the new graph. This suggests that a horizontal translation of one unit to the right has been applied to the original function.
Similarly, the point (2, -1) on the original square root function has been transformed to the point (3, -4) on the new graph. This suggests that a vertical translation of three units downward has been applied to the original function.
Therefore, the equation for the function represented by the graph is:
y = √(x - 1) - 3
where the x - 1 term inside the square root function represents the horizontal translation of one unit to the right, and the -3 outside the square root function represents the vertical translation of three units downward.