Calculus and Its Applications, Chapter 1, 1.1, Section 1.1, Problem 56

Illustrate the function
$
G(x) =
\left\{
\begin{equation}
\begin{aligned}
-x &+ 3, & \text{for } x < 2,\\
x &+ 1, & \text{for } x \geq 2.
\end{aligned}
\end{equation}
\right.
$ and then determine the limit
$\displaystyle \lim_{x \to 2^-} G(x) \text{ and } \lim_{x \to 2^+} G(x) \text{ and } \lim_{x \to 2} G(x)$.
If necessary, state the limit if it does not exist.




Based from the graph, the $\displaystyle \lim_{x \to 2^-} G(x) = 1 \text{ and the }\lim_{x \to 2^+} G(x) = 3$.
Thus, the $\displaystyle \lim_{x \to 2} G(x)$ does not exist because the $\displaystyle \lim_{x \to 2^-} G(x)$ is equal
to the $\displaystyle \lim_{x \to 2^+} G(x)$.