Write a rule for the function whose graph can be obtained from the given parent function by performing the given transformations. Parent function: f(x)=[x]. Transformations: shift the graph 6 units to the right, stretch it vertically by a factor of 2 and shift it downward 3 units

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.