Answer
Domain: $x\geq -\frac{5}{3}$
Range: $y\geq 0$
Work Step by Step
Given \begin{equation}
f(x)=\sqrt{3 x+5}.
\end{equation} The radicand of a radical function must be positive. This means that we must have $$3 x+5\geq 0\implies x\geq -\frac{5}{3}.$$ Also, we see that the function's value $\sqrt{3x+5}\geq 0$, therefore $y\geq 0$.
The domain and range of the given function are: \begin{equation}
\begin{aligned}
\textbf{Domain :}\quad & x\geq -\frac{5}{3}\\
\textbf{Range :}\quad & y\geq 0\\\\
\end{aligned}
\end{equation}
