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Question: What is Region ?

Answer:

A Circle drawn on a page divides it into two regions, that part of the surface inside the circle and that part outside. When a network is drawn on a piece of paper it will divide it into a number of regions each bounded by arcs.

In the example there are 6 regions, 5 inside the network and one region outside.

When a graph is drawn for an equation such as x + y = 6, the line representing it divides the plane into two regions which corresponds to the inequalities x + y > 6 and x + y < 6 . Equations such as y = x2 divide the plane in a similar way but this time the boundary line is a parabola.