For y=k/x, this is an inverse proportional function, and its images are two hyperbolas in the first and third quadrants respectively. The image is infinitely close to the X axis and the Y axis, but never intersects the axes.
For y = k/(1 of x-3), it is obtained by moving the whole y=k/x image to the right by 1 unit.
And y = 5/3+k/(x- 1), and its image moves up by 5/3 units.
So the function is like a hyperbola infinitely close to the straight line x= 1/3 and infinitely close to y=5/3.
Draw X belongs to this diagram, as shown in the figure. As can be seen from the figure, the straight line Y = below 5/3, the maximum value is f(- 1), and the straight line Y = above 5/3, the minimum value is f(3), so the answer is: y≤f(- 1) or y≥f(3).