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.