Let's go through each question based on the graph:

1. For what values of $x$ is the function positive?

   • The function is positive when its graph is above the x-axis. From the graph, this occurs approximately between $x \in (-5, -2)$ and $x \in (2, 5)$.

2. For what values of $x$ is the function negative?

   • The function is negative when the graph is below the x-axis. This happens when $x \in (-\infty, -5)$ and $x \in (-2, 2)$, and again for $x \in (5, \infty)$.

3. For what values of $x$ does the function reach a relative minimum?

   • The function reaches a relative minimum at the lowest points of the valleys. From the graph, this occurs around $x = 0$ (approximately at $y = -5$).

4. For what value of $x$ does the function reach a relative maximum?

   • A relative maximum occurs at the peak of the curve. This happens around $x = -3.5$ and $x = 3.5$, where the graph reaches its highest points between the valleys.

5. For what values of $x$ is the function increasing?

   • The function is increasing when the graph moves upwards as $x$ increases. From the graph, this occurs for $x \in (-\infty, -3.5)$, $x \in (0, 3.5)$, and for $x > 5$.

6. For what values of $x$ is the function decreasing?

   • The function is decreasing when the graph moves downwards as $x$ increases. This happens for $x \in (-3.5, 0)$ and $x \in (3.5, 5)$.

7. Describe what happens to the value of $f(x)$ as $x$ gets very large.

   • As $x \to \infty$, the graph rises sharply, indicating that $f(x) \to \infty$.

8. Describe what happens to the value of $f(x)$ as $x$ gets very negative.

   • As $x \to -\infty$, the graph also rises sharply, implying that $f(x) \to \infty$.

If you have any questions or want further details, feel free to ask!

Here are 5 follow-up questions:

1. What does it mean for a function to have a relative minimum and maximum?
2. How can we algebraically determine intervals of increase or decrease in a function?
3. Why does the function behave symmetrically as $x \to \infty$ and $x \to -\infty$?
4. How do relative extrema help us understand the overall shape of a function?
5. What types of functions exhibit similar behavior at $x \to \infty$ and $x \to -\infty$?

Tip: Always check the signs of the function's derivative to confirm where it is increasing or decreasing!