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Let's analyze the graph of the function \( f(x) \) to find its domain and range.

### (a) Domain of \( f(x) \):
The domain is the set of all possible \( x \)-values for which the function is defined. From the graph:
- The curve starts from an \( x \)-value of around \( -10 \) (leftmost part of the graph) and continues to \( x = -5 \), with an open circle at \( x = -5 \), meaning the function is not defined at \( x = -5 \).
- After \( x = -5 \), there is a discontinuity, and the function reappears from around \( x = 1 \) to \( x = 6 \), again with an open circle at \( x = 6 \).

Thus, the domain of \( f(x) \) is:
\[
(-10, -5) \cup (1, 6)
\]

### (b) Range of \( f(x) \):
The range is the set of all possible \( y \)-values that the function can take. From the graph:
- The highest \( y \)-value occurs around \( y = 10 \) at \( x = -10 \).
- The lowest point on the graph is at \( y = -10 \) where there is a flat line between \( x = 1 \) and \( x = 6 \).

Thus, the range of \( f(x) \) is:
\[
[-10, 10]
\]

### Final Answers:
- **Domain**: \( (-10, -5) \cup (1, 6) \)
- **Range**: \( [-10, 10] \)

Let me know if you'd like any more details or have further questions!

### Related Questions:
1. How would the domain change if there was no open circle at \( x = -5 \)?
2. What is the significance of open and closed circles in defining the domain and range?
3. How can we determine whether a function is continuous from its graph?
4. What happens to the range if the graph is shifted vertically by 3 units?
5. Can the domain or range include infinity in real-world applications?

**Tip**: Open circles on a graph indicate values that are excluded from the domain or range, while closed circles show included values.

Given the graph of f(x) above, find the following and write your answer in interval notation:

(a) Domain of f(x)
(b) Range of f(x)

Learn how to determine the domain and range of a function from its graph using interval notation. This problem includes identifying where the function is defined and the values it can take, as well as understanding open and closed intervals in graphing.

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