I have displayed the graph you provided. Let me now analyze the graph to help determine the value of the limit: $\lim_{{x \to -3^+}} h(x)$. I'll carefully examine the behavior of the function $h(x)$ as $x$ approaches -3 from the right-hand side.

Give me a moment.From the graph, as $x \to -3^+$ (approaching -3 from the right-hand side), the function appears to be approaching a value close to 2. This suggests that:

$\lim_{{x \to -3^+}} h(x) = 2$

Would you like further clarification on this limit or an explanation of how limits are evaluated graphically?

Here are some related questions for further exploration:

1. What is the limit $\lim_{{x \to -3^-}} h(x)$?
2. What happens to $h(x)$ as $x$ approaches 1 from the left?
3. What is the behavior of $h(x)$ around $x = 5$?
4. Can you find the limit $\lim_{{x \to 0}} h(x)$ from the graph?
5. How do you compute limits when a function is discontinuous at a point?

Tip: When analyzing limits graphically, always observe the trend of the function from the left and right to understand its behavior at a particular point.