Exercise 30 Page 120

Let's start by graphing the boundary line for the given inequality. Inequality & Boundary Line y ≥ [ [ x ] ] & y = [ [ x ] ] The Output of the above function is the greatest integer less than or equal to x. For example, [ [ 2.1 ] ] =2, [ [ 2.9 ] ] =2, and [ [ -1.7 ] ] =-2.

Now, we need to test which region is the one that satisfies the inequality. Let's use (2,0) as our test point. If it produces a true statement, we will shade the region that contains (2,0). If not, we will shade the other region.

Since 0 is not greater than or equal to 2, we will shade the region which does not contain the point (2,0). Note that the inequality is not strict, so the horizontal segments will be solid.

Finally, we need to determine whether the vertical boundaries will be solid or dashed. To do so, we will use (1,0.5) to test the left boundaries. Let's do it!

Since the point (1,0.5) produced a false statement, all the vertical boundaries will be dashed.