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Consider a rectangular coordinate system in the plane, in the usual sense of analytic geometry. Every...

Consider a rectangular coordinate system in the plane, in the usual sense of analytic geometry. Every point has a pair of coordinates (x,y). For the purposes of this question, let us regard points as indistinguishable from the ordered pairs (x, y) that describe them. Thus every figure, that is, every set of points, becomes a collec- tion of ordered pairs of real numbers. Under what conditions, if any, do the following figures represent functions? (a) a triangle, (b) a single point, (c) a line, (d) a circle, (e) a semicircle, including the endpoints, (f) an ellipse. What, in general, is the geometric condition that a figure in the coordinate plane must satisfy to be a function? (Very rigorous arguments are not required - just give the idea intuitively for each).

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milcah answered 1 year ago
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