Describe and represent the set of points in R3 that satisfies 0<(or equal to)y<(or equal to)6

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nathanshields eNotes educator| Certified Educator

Imagine a traditional x-y plot where `0<=y<=6`
It would have two solid horizontal lines through y = 0 and y = 6, with the area in between them shaded.

In other words, the vertical line segment from (0,0) to (0,6) is swept parallel to the x-axis, since any x-values are game (x is not in the relation).

So now imagine this area (like an infinitely long rectangle) ALSO swept up, parallel to the z-axis, to form a "box" infinitely long in two dimensions, but only 6 units wide in one dimension (y). 

You could imagine an infinitely huge swimming pool only six inches deep.  I hope this helps!