U can visualise it by drawing the before and after transformed graphs to compare in order to deduce the answer.
From the picture, you will realise that when x is unchanged, I'm this case I'm using points x=0 and x=13, the value of the y coordinate in the transformed graph (y = x-13) actually decreased by 13 units as compared to the original graph of y=x.
Hence the graph actually got translated 13 units in the direction of negative y axis which is option D