The function $h(x)$ is piecewise, so we need to analyze the value of $h(x)$ at $x = 2$ based on the segments provided.

• The first segment is from $(-4, 3)$ to $(0, 2)$, with both endpoints closed. This segment is irrelevant since it doesn't include $x = 2$.

• The second segment goes from $(2, 3)$ to $(4, 5)$, with an open circle at $(2, 3)$ and a closed circle at $(4, 5)$. Since the point at $x = 2$ is open, this means $h(2)$ is not defined at 3.

Thus, the function has no defined value at $x = 2$, and the correct value of $h(2)$ is:

$h(2) = 0$

Want more details or have questions about this?

Here are 5 follow-up questions:

1. What happens to $h(x)$ if we change the open point at $x = 2$ to closed?
2. Can you represent this piecewise function algebraically?
3. How do open and closed points affect the continuity of a function?
4. What would $h(x)$ be at $x = 4$?
5. How would the graph change if $h(2)$ were defined as 3?

Tip: In piecewise functions, always check whether endpoints are open or closed when determining specific values.