The image shows a piecewise function $h(x)$, represented graphically. Let's address each part of the question based on the graph:

A) Find $h(0)$

From the graph, locate $x = 0$. At this point, the function has a closed dot at $(0, -5)$, which means the value of $h(0)$ is: $h(0) = -5$

B) Find $h(4)$

At $x = 4$, follow the graph. The point at $x = 4$ on the function corresponds to $(4, 1)$. Therefore, the value of $h(4)$ is: $h(4) = 1$

C) Find $h(-2)$

At $x = -2$, trace the graph to the corresponding point. The point at $x = -2$ lies on the straight part of the graph (the linear section). By observing the graph, $h(-2)$ corresponds to $(-2, 3)$, so: $h(-2) = 3$

Summary of values:

• $h(0) = -5$
• $h(4) = 1$
• $h(-2) = 3$

Would you like more details or further clarifications?

Follow-up Questions:

1. What is the slope of the line on the left side of the graph?
2. How would you define the domain of the given function?
3. What is the range of the function based on the graph?
4. How would the graph change if the right branch extended further?
5. How can we express the function $h(x)$ as a piecewise function?

Tip:

Always pay attention to open and closed dots in graphs; they indicate whether a point is included or excluded from the function.