Subjects algebra

Real Solutions

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Real Solutions


1. **State the problem:** We need to find all real solutions to the equation $f(x) = 0$, which correspond to the points where the graph of $y = f(x)$ crosses the x-axis. 2. **Analyze the graph:** Given the continuous function $f(x)$ with the described behavior: - It crosses the x-axis between $x = -3$ and $x = -2$. - It crosses again at $x \approx 4$. - A final crossing occurs between $x = 8$ and $x = 9$. 3. **Approximate the x-intercepts:** - First root near $x \approx -2.5$ - Second root near $x = 4$ - Third root near $x \approx 8.5$ 4. **Conclusion:** These are the three approximate real solutions of $f(x) = 0$ based on the graph: $$x \approx -2.5, \quad x = 4, \quad x \approx 8.5$$ These points represent where the curve crosses the x-axis.