Now we will make a table of values, using a variety of values for x greater than or equal to 2.
x
sqrt(x-2)
y=sqrt(x-2)
2
sqrt(2-2)
0
3
sqrt(3-2)
1
4
sqrt(4-2)
≈ 1.41
5
sqrt(5-2)
≈ 1.73
6
sqrt(6-2)
2
7
sqrt(7-2)
≈ 2.24
8
sqrt(8-2)
≈ 2.45
Let's plot the points and connect them with a smooth curve.
Finally, we can determine the region to shade using a test point. If the test point produces a true statement when substituted into the given inequality, we will shade the region that contains it. If it produces a false statement, we will shade the region which does not contain the test point. We will use the point (3,0).
Since the point produced a true statement, we will shade the region that contains (3,0). Note that we are not given a strict inequality, so the curve will be solid.
