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The graph you provided represents a function \( y = f(x) \), and the question asks for the real solutions of \( f(x) = 0 \). To find the solutions, we need to identify the points where the graph crosses the x-axis, as these are the points where \( f(x) = 0 \).

From the graph, the x-intercepts (where the graph crosses the x-axis) are approximately:

- \( x = -3 \)
- \( x = 1 \)
- \( x = 5 \)

Thus, the real solutions to \( f(x) = 0 \) are:
\[
x = -3, \quad x = 1, \quad x = 5
\]

Would you like a deeper explanation or have any questions?

Here are 5 related questions to further explore the topic:
1. What is the significance of the points where the graph crosses the x-axis?
2. How can you algebraically solve for \( f(x) = 0 \) if you have the equation for \( f(x) \)?
3. What is the difference between real and complex solutions for equations like \( f(x) = 0 \)?
4. How would you determine the multiplicity of a root by looking at the graph?
5. Can a polynomial function of degree 3 (like this graph) have more or fewer than 3 real solutions?

**Tip:** The x-intercepts of a function correspond to its real roots (solutions), while the behavior of the graph at these points can help you determine if the root has even or odd multiplicity.

The graph of y = f(x) is shown. What are all of the real solutions of f(x) = 0?

Learn how to identify the real solutions of f(x) = 0 by analyzing the x-intercepts of a graph. This algebraic problem involves key concepts in interpreting function graphs and understanding real roots, suitable for high school students.

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