https://file.aiquickdraw.com/mathbot/file/172844929146336qjv8qd.jpg

The question asks you to find the solution set where \( f(x) > 0 \) based on the provided graph.

### Steps to solve:
1. **Interpret the graph**: We need to look for the intervals where the function is above the x-axis, as that represents \( f(x) > 0 \).
2. **Critical points**: The function crosses the x-axis at \( x = -2 \), \( x = 0 \), and \( x = 2 \). These are points where \( f(x) = 0 \), so these will help define the boundaries of the intervals.
3. **Check the intervals**:
   - Between \( x = -2 \) and \( x = 0 \), the graph is above the x-axis, so \( f(x) > 0 \).
   - Between \( x = 0 \) and \( x = 2 \), the graph is below the x-axis, so \( f(x) < 0 \).
   - After \( x = 2 \), the graph is again above the x-axis, so \( f(x) > 0 \).

### Solution in interval notation:
For \( f(x) > 0 \), the intervals where the graph is above the x-axis are:
\[
(-2, 0) \cup (2, \infty)
\]

Let me know if you'd like more details or have any questions!

### Related questions:
1. How do you solve inequalities graphically in general?
2. What does it mean for a function to be greater than or less than 0 in different intervals?
3. How can you use the derivative of a function to determine where it is positive or negative?
4. How do you write compound inequalities in interval notation?
5. What is the difference between open and closed intervals in solutions?

**Tip**: Always identify where the graph crosses the x-axis to determine changes in the sign of \( f(x) \).

Use the graph of the function f to solve the inequality. (a) f(x) > 0

Learn how to solve the inequality f(x) > 0 using the provided graph. This problem explores the concepts of graphical inequalities and interval notation, focusing on where the function crosses the x-axis. Suitable for Grades 10-12 students.

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