3. $lim_{x\rightarrow1}g(x)=$

Explanation:

Step1: Recall limit definition

The limit as $x$ approaches $a$ of a function $y = g(x)$ is the value that $g(x)$ approaches as $x$ gets arbitrarily close to $a$ (from both the left - hand and right - hand sides).

Step2: Analyze left - hand and right - hand limits

Looking at the graph of $y = g(x)$ as $x$ approaches $1$ from the left - hand side ($x\to1^{-}$), $g(x)$ approaches $2$. As $x$ approaches $1$ from the right - hand side ($x\to1^{+}$), $g(x)$ also approaches $2$.

Answer:

$2$