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For the function 𝑓(𝑥) graphed below, solve the inequality 𝑓(𝑥) > 0 and answer in interval notation:

To solve the inequality \( f(x) > 0 \) using the given graph, we need to identify the intervals where the function's output is positive, meaning the graph is above the x-axis.

Based on the points plotted on the graph:

1. The point \((-3, 4)\) indicates \( f(-3) = 4 \), which is positive.
2. The point \((-2, 2)\) indicates \( f(-2) = 2 \), which is positive.
3. The point \((2, 3)\) indicates \( f(2) = 3 \), which is positive.
4. The point \((3, 2)\) indicates \( f(3) = 2 \), which is positive.

The other points indicate values where \( f(x) \leq 0 \).

Now, we determine the intervals:

- From the points, we see that the function is above the x-axis from \( x = -3 \) to \( x = -2 \) and from \( x = 2 \) to \( x = 3 \).
  
Therefore, the solution to the inequality \( f(x) > 0 \) is:

\[
(-3, -2) \cup (2, 3)
\]

**Would you like more details or have any questions about this solution?**

Here are five related questions you might consider:

1. How can you determine if a function is positive using its graph?
2. What does it mean when a function is below the x-axis?
3. How would you solve the inequality \( f(x) < 0 \) for the same function?
4. What does the point \( (0, -1) \) tell you about the function's value at \( x = 0 \)?
5. How can you find where \( f(x) = 0 \) using the graph?

**Tip:** When working with inequalities involving functions, always pay attention to the intervals where the function changes sign, as these are crucial for determining where the function is positive or negative.

Learn how to solve the inequality f(x) > 0 using graph analysis. Understand the intervals where the function is positive by analyzing its graph. Suitable for students in Grades 9-12.

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