https://file.aiquickdraw.com/mathbot/file/17271882131998mfwp3oy.jpg

The problem displayed asks: "Find all values of \( x \) for which \( f(x) > 0 \)" based on the graph of the function \( f(x) \) shown.

### Analysis:

From the graph, you need to determine where the function \( f(x) \) is greater than zero (i.e., where the graph is above the x-axis). Here's how to analyze it:

1. **Identify the x-intercepts**: The points where the graph crosses the x-axis are the values of \( x \) where \( f(x) = 0 \).
   
2. **Determine intervals where \( f(x) > 0 \)**: Look for sections of the graph that lie above the x-axis. These will be the intervals of \( x \) for which \( f(x) > 0 \).

### Based on the graph in the image:
- The function appears to cross the x-axis at two points. Let’s approximate these points.
   - The graph crosses the x-axis at around \( x = -2 \) and \( x = 2 \).

### Conclusion:
- The function is positive (i.e., \( f(x) > 0 \)) for the interval **between** the two x-intercepts, meaning \( f(x) > 0 \) for \( -2 < x < 2 \).

Thus, the solution is:

\[
-2 < x < 2
\]

Would you like further details or have any questions? Here are some related questions you might find useful:

1. How do we calculate x-intercepts algebraically?
2. What is the difference between \( f(x) > 0 \) and \( f(x) \geq 0 \)?
3. How would this change if the function were shifted vertically?
4. What happens if the function dips below the x-axis for a larger interval?
5. How do you determine concavity from the graph?

**Tip**: Always check the points where the function crosses the x-axis carefully, as they help you determine when a function is positive or negative.

Find all values of x for which f(x) > 0 based on the graph of the function f(x).

Learn how to find all values of x for which f(x) is greater than 0 by analyzing a quadratic graph. This problem covers graphing concepts, inequalities, and x-intercepts. Suitable for students in Grades 8-10.

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