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.