From the graph provided, we need to determine the value of $h(2)$.

Step-by-step solution:

1. Locate $x = 2$ on the horizontal axis.
2. Trace vertically at $x = 2$ to find the corresponding value of $h(x)$ (on the vertical axis).
3. At $x = 2$, the graph shows an open circle at $h(x) = 1$, which indicates that $h(2)$ is not defined at 1.
4. However, moving further, the graph dips to $h(x) = -3$ at $x = 2$, represented by a filled point. This indicates that $h(2) = -3$.

Final Answer:

$h(2) = -3$

Would you like more details or explanations? Here are some related questions to deepen understanding:

1. What does an open circle on a graph represent in terms of function values?
2. How can you identify the domain of a piecewise function from its graph?
3. Why is the filled point at $x = 2$ the valid value for $h(2)$?
4. How would the graph change if $h(2)$ were instead defined at $h(x) = 1$?
5. What is the importance of distinguishing open and closed circles in evaluating functions?

Tip: Always double-check for open and closed points when interpreting graphs of piecewise functions to avoid errors in determining function values.