Consider a rectangular coordinate system in the plane, in theusual sense of analytic geometry. Every point has a pair ofcoordinates (x,y). For the purposes of this question, let us regardpoints as indistinguishable from the ordered pairs (x, y) thatdescribe them. Thus every figure, that is, every set of points,becomes a collec- tion of ordered pairs of real numbers. Under whatconditions, if any, do the following figures represent functions?(a) a triangle, (b) a single point, (c) a line, (d) a circle, (e) asemicircle, including the endpoints, (f) an ellipse. What, ingeneral, is the geometric condition that a figure in the coordinateplane must satisfy to be a function? (Very rigorous arguments arenot required - just give the idea intuitively for each).
