Let's analyze this graph and the questions provided.

Part A) Understanding $f(x) > 0$

In the graph, $f(x) > 0$ means the values where the graph is above the x-axis (the line $y = 0$).

So, the correct choice is "above the x-axis".

Part B) Finding values of $x$ where $f(x) > 0$

To answer this part, we need to determine where the graph lies above the x-axis:

• The graph is positive (above the x-axis) in two regions:
  • On the left side, starting from $x = -\infty$ and stopping at $x \approx -5.5$.
  • On the right side, for $x > 2$.

Thus, the solution is: $(-\infty, -5.5) \cup (2, \infty)$

Part C) Finding values of $x$ where $f(x) < 0$

Here, $f(x) < 0$ means finding where the graph is below the x-axis. Observing the graph, this happens between:

• $x \approx -5.5$ and $x = 2$.

Thus, the interval is: $(-5.5, 2)$

Do you need more detailed explanations, or have any questions on this so far?

Here are 5 follow-up questions to deepen understanding:

1. Why is $f(x) = 0$ at the points where the graph touches the x-axis?
2. How do you interpret $f(x)$ in terms of real-world applications, such as physics or economics?
3. How would you write the solution to $f(x) = 0$?
4. Can you estimate the exact coordinates where the function crosses the x-axis?
5. How does the behavior of the graph at the asymptotes influence the intervals?

Tip: When solving inequalities involving functions, always check the graph’s interaction with the x-axis to determine positive and negative regions.