Answer
$$\lim_{x \to 3 }g(x)=-1$$
Work Step by Step
Please note that the graph of $g(x)$ is the graph of $f(x)$ shifted down two units.
To find $\lim_{x\to 3 }g(x)$, examine the graph of $g$ near $x=3$. As $x$ gets closer to $3$, the values of $g(x)$ get closer to $-1$. We conclude from the graph that$$\lim_{x \to 3 }g(x)=-1.$$
