Answer
$g(x)$ is discontinuous from the left at $x=3$ and hence, is not continuous on $[-1,3]$.
Work Step by Step
The exercises 1-4 mention the appearance of "breaks" as a sign of discontinuities in the graph, which we shall prove later on.
The graph of $g(x)$ in Exercise 2 has a break at $x=3$. $g(3)$, as seen in the graph, equals $1.5$.
We also notice that as $x$ approaches $3$ from the left, $g(x)$ approaches $1$. So $\lim_{x\to3^-}g(x)=1$
Because $\lim_{x\to3^-}g(x)\ne g(3)$, according to definition, $g(x)$ is discontinuous from the left at $x=3$ and hence, is not continuous on $[-1,3]$.
