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To determine the **domain** and **range** of the given function \( f(x) \) from the graph:

### Domain:
The **domain** is the set of all possible input values (i.e., \( x \)-values) for which the function is defined. From the graph, we can observe the following:

1. The function starts at \( x = -10 \) (closed point), continues to \( x = -5 \) (open point).
2. Then, there’s a line segment starting at \( x = -5 \) (closed point) to \( x = 0 \) (open point).
3. Finally, the function exists from \( x = 0 \) to \( x = 5 \) (open at both ends).

Therefore, the domain is:
\[ \boxed{[-10, -5) \cup [-5, 0) \cup (0, 5)} \]

### Range:
The **range** is the set of all possible output values (i.e., \( y \)-values) that the function can take. From the graph, we can observe:

1. In the first segment, the \( y \)-values remain constant at \( y = -5 \).
2. For the second piece, the function moves from \( y = -5 \) up to \( y = 5 \), reaching the maximum value of 5 and then dropping back to 0.
3. Finally, the third segment dips down to \( y = -5 \) from \( y = 5 \).

Therefore, the range is:
\[ \boxed{[-5, 5]} \]

### Recap:
- **Domain**: \( [-10, -5) \cup [-5, 0) \cup (0, 5) \)
- **Range**: \( [-5, 5] \)

Let me know if you'd like further clarification or details!

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Here are five related questions to expand your understanding:
1. What is the significance of an open versus closed point on a graph?
2. How do you determine whether a function is continuous from its graph?
3. Can a function have gaps in its domain? What causes these gaps?
4. How does the graph of a function inform us about its behavior as \( x \to \infty \)?
5. How does symmetry in the graph of a function affect its domain and range?

**Tip**: Always pay attention to open and closed points when determining the domain and range from a graph, as they indicate whether an endpoint is included.

Learn how to find the domain and range of the function f(x) using a graph. This problem explores how to determine the valid x-values (domain) and y-values (range) from visual data. Suitable for Grades 9-11 students learning about functions and graph analysis.

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