The correct answer is D. y-1=|x-5|.
The graph shows a V-shaped curve that is shifted down one unit and shifted to the right five units. The absolute value function has this characteristic V-shape, and the equation for the graph of the absolute value function is y=|x|.
To shift the graph down one unit, we subtract 1 from both sides of the equation, giving us y-1=|x|. To shift the graph to the right five units, we add 5 to both sides of the equation, giving us y-1=|x+5|.
The other answer choices are incorrect because they do not produce the same graph as the image. For example, the graph of y+1=|x-5| would be shifted up one unit and shifted to the right five units, which is not the same as the graph in the image.
Complete question:
Identify the equation for the graph. A. y+1=|x-5| B. y+1=|x+5| C. y-1=|x+5| D. y-1=|x-5|