Answer:
See the attached figure.
Step-by-step explanation:
The given function is called piecewise function which is the function that can be in pieces, i.e: defined by multiple sub-functions.
[tex]f(x)=\left \{ {{2x} \ , \ x\geq3 \atop {-\frac{1}{3}x+7 \ , \ x\leq 3 }} \right.[/tex]
So, need to graph 2x in the interval [3,∞)
And graph -(1/3) x + 7 in the interval (-∞,3]
We will find that f(3) at the function 2x will be equal f(3) at the function -(1/3) x + 7
Which mean the function is continuous.
The attached figure represents the graph of function, it was graphed using the tables on the graph.
