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The problem asks to find the solution set where \( f(x) < 0 \) by using the given graph of \( y = f(x) \).

Looking at the graph:
- \( f(x) \) represents a parabola that opens downward.
- The parabola intersects the x-axis at two points, approximately at \( x = -2 \) and \( x = 2 \).
- The region where \( f(x) < 0 \) is when the graph is below the x-axis.

From the graph, the function is negative (below the x-axis) between the x-values \( x = -2 \) and \( x = 2 \). Thus, the solution set in interval notation is:

\[
(-2, 2)
\]

This interval represents the x-values for which \( f(x) < 0 \).

Would you like further details or clarification?

Here are 5 related questions to expand this topic:
1. What is the solution set if \( f(x) > 0 \)?
2. How would you find the x-intercepts of \( f(x) \) algebraically?
3. Can the vertex of the parabola help in solving inequalities?
4. How does changing the direction of the parabola affect the solution for \( f(x) < 0 \)?
5. What other methods besides graphing could be used to solve inequalities involving functions?

**Tip:** Always check the intervals where the function crosses the x-axis when solving inequalities using a graph.

Solve the inequality f(x) < 0 based on the given graph of y = f(x).

Learn how to solve inequalities using the graph of a quadratic function. This problem focuses on identifying the solution set for f(x) < 0 by analyzing where the graph lies below the x-axis. Suitable for students in Grades 8-10.

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