Question

How do I graph this? In picture below
please include the graph

Answer 1

See the attached figure.

Explanation:

The given function is called piecewise function which is the function that can be in pieces, i.e: defined by multiple sub-functions.

`f(x)=\left \{ {{2x} \ , \ x\geq3  \atop {-(1)/(3)x+7 \ , \ x\leq 3 }} \right.`

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.