Answer
See the graph
Work Step by Step
We are given: $f(x)=\frac{1}{3}x+6$
Domain: $x \geq -6 \rightarrow [-6,+\infty)$
For $x=-6 \rightarrow y=4$
From the graph, you can see that the range is $y\gt4$. The graph is unbroken, so the function is continuous.