We want to graph the given radical function. g(x)=5x−3 To do so, we will start by making a table of values. Recall that the radicand cannot be negative. With this in mind, we can first determine its domain as shown below. x−3≥0⇔x≥3 Therefore, we will use x-values greater than or equal to 3. Let's start!
x | 5x−3 | g(x)=5x−3 |
---|---|---|
3 | 53−3 | 0 |
4 | 54−3 | 0.2 |
5 | 55−3 | 0.282… |
6 | 56−3 | 0.346… |
7 | 57−3 | 0.4 |
The ordered pairs (3,0), (4,0.2), (5,0.282), (6,0.346), and (7,0.4) all lie on the graph of the function. Now, we will plot and connect these points with a smooth curve.
We can see above that the graph of the function goes to infinity in the positive direction. Therefore, its range are all values greater than or equal to 0. Domain:Range: x≥3 y≥0