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)+3
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.
x≥ 0
Now we will make a table of values, using a variety of values for x greater than or equal to 0.
x
sqrt(x)+3
y
0
sqrt(0)+3
3
1
sqrt(1)+3
4
2
sqrt(2)+3
≈ 4.414
3
sqrt(3)+3
≈ 4.732
4
sqrt(4)+3
5
5
sqrt(5)+3
≈ 5.236
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 (4,6).
Since the point produced a true statement, we will shade the region that contains (4,6). Note that we are not given a strict inequality, so the curve will be solid.
