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How does one find the union and intersection of two inequalities by shading regions in a graph? For instance, find the union and intersection of $y \lt 3$ and $x \ge 2$?

Ishfaaq
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user34039
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    Draw the graphs for $y = 3$ and $x = 2$. Take a few points on these lines and see in what direction you need to go to get the relevant inequalities.. – Ishfaaq Feb 19 '14 at 08:55

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First draw the line $y=3$. It will separate the plane into two regions: shade the entire region which contains the points $(x,y)$ such that $y<3$.

(If you are not sure on which side of the line that region is, pick any side and choose any point on that side. Replace the values of the coordinates of the chosen point in the inequality. If the inequality is true for these values, shade that side. Otherwise, shade the other side.)

Repeat with the other inequality, probably using other colors or marks to avoid confusion. Pretend the previous line and shading aren't there. The drawings will most probably overlap.

Now: the intersection will be the region which is shaded by both colors or marks. The union will be the whole region which is covered by at least one color or mark.

This can be extended to any number of inequalities.

dafinguzman
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