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Notice that the minimum distance from the origin to this function is a 45∘ line from (0,0) to (1,1) or (-1,-1). Let's add this to the graph.
If we zoom in on one of the quadrants, we notice that the distance is the hypotenuse of a 45∘-45∘-90∘ triangle. In such a triangle the hypotenuse is always 2 longer than any of the legs. Since the legs are both 1 unit long, the hypotenuse must be 2 units.
As we can see, when the constant of variation is 1 the function passes through (1,1). If we can push this graph outward so that the closest point to the origin is (4,4), we will have a reciprocal function with a minimum distance of 42 units. This is because this point creates a 45∘-45∘-90∘ triangle with a leg length of 4.