Let's analyze the graph and answer the questions based on the function $h(x)$:

a. $h(0)$:

To find $h(0)$, look at the value of the function when $x = 0$. From the graph, at $x = 0$, the value of $h(x)$ is approximately 0.5. Thus, $h(0) = 0.5$.

b. $h(4)$:

To find $h(4)$, check the value of the function at $x = 4$. At $x = 4$, the graph shows an open circle at $y = 3$, which means $h(4)$ is not defined. Thus, $h(4)$ is undefined.

c. Solve $h(x) = -1$:

To solve $h(x) = -1$, find the points where the graph of $h(x)$ crosses $y = -1$. From the graph, $h(x) = -1$ at $x = -1$ and $x = 1$. So, the solutions are $x = -1$ and $x = 1$.

d. Solve $h(x) = 5$:

To solve $h(x) = 5$, find the points where the graph of $h(x)$ reaches $y = 5$. From the graph, there is no point where the graph reaches $y = 5$, so there is no solution for $h(x) = 5$. Thus, there is no solution.

Would you like more details or have any further questions?

Here are 5 related questions to explore:

1. What are the zeros of the function $h(x)$?
2. What is the range of the function based on the graph?
3. Is the function $h(x)$ continuous? Why or why not?
4. What are the local maximum and minimum points of $h(x)$?
5. Can you find the domain of the function?

Tip: When analyzing graphs of functions, look closely for open and closed circles to identify whether points are included or excluded from the function's values.