Start by drawing the boundary curve. Recall that the domain of radical functions only includes values for which the radicand is non-negative.
Practice makes perfect
To graph the given inequality, we will start by drawing its boundary curve.
y=- sqrt(x-1)+2
To do so, we first need to find the domain. For radical functions, the domain only includes values for which the radicand is non-negative.
Now we will make a table of values, using a variety of values for x greater than or equal to 1.
x
- sqrt(x-1)+2
y
1
- sqrt(1 -1)+2
2
2
- sqrt(2 -1)+2
1
3
- sqrt(3 -1)+2
≈ 0.586
4
- sqrt(4 -1)+2
≈ 0.268
5
- sqrt(5 -1)+2
0
6
- sqrt(6 -1)+2
≈ - 0.236
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 (2,0).
Since the point did not produce a true statement, we will shade the region that does not contain (2,0). Note that we are given a strict inequality, so the curve will be dashed.
