Graphing Radical Functions

We want to graph the given radical function. $$\begin{array}{c}g(x)=\frac{\sqrt{x-3}}{5}\end{array}$$ 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. $$\begin{array}{c}x-3\ge 0\iff x\ge 3\end{array}$$ Therefore, we will use $x\text{-}$values greater than or equal to $3.$ Let's start!

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 $0.$ $$\begin{array}{rl}\text{Domain:}& x\ge 3\\ \text{Range:}& y\ge 0\end{array}$$