https://file.aiquickdraw.com/mathbot/file/1729054949549a4cjwjue.jpg

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:
\[ (-5.5, 2) \]

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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.

A graph is shown, and the user is asked to solve f(x) > 0, which means finding the intervals where the graph is above the x-axis. The user is also asked to solve f(x) < 0, meaning where the graph is below the x-axis.

Analyze a graph to find the intervals where the function f(x) is positive (above the x-axis) and negative (below the x-axis). This involves function graphing and solving inequalities, suitable for students in Grades 9-12.

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