To find the limit of $h(x)$ as $x$ approaches 4, we need to analyze the graph you've provided near $x = 4$. Here's the breakdown:

• As $x$ approaches 4 from the left ($x \to 4^-$), the graph of $h(x)$ descends toward $h(x) = -4$.
• As $x$ approaches 4 from the right ($x \to 4^+$), the graph rises toward $h(x) = -4$.

Since both the left-hand and right-hand limits approach $-4$, we conclude that:

$\lim_{x \to 4} h(x) = -4$

Would you like more details on limit behavior or any other part of the graph explained?

Here are 5 related questions that expand on this concept:

1. What is the limit of $h(x)$ as $x$ approaches 0?
2. Does the limit of $h(x)$ exist as $x$ approaches -6?
3. Is $h(x)$ continuous at $x = 4$? Why or why not?
4. What is the value of $h(4)$, and how does it compare to the limit?
5. How would you determine whether $h(x)$ is differentiable at $x = 4$?

Tip: When determining limits from a graph, always check both the left-hand and right-hand behavior to ensure the function approaches the same value from both directions.