Answer
$$\lim_{x \to 1 }g(x)=-\frac{3}{2}$$
Work Step by Step
Please note that the graph of $g(x)$ is the graph of $f(x)$ horizontally stretched by $\frac{1}{2}$.
To find $\lim_{x\to 1 }g(x)$, examine the graph of $g$ near $x=1$. As $x$ gets closer to $1$, the values of $g(x)$ get closer to $-\frac{3}{2}$. We conclude from the graph that$$\lim_{x \to 1 }g(x)=-\frac{3}{2}.$$
