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.