https://file.aiquickdraw.com/mathbot/file/1724942996923oyzj4fhf.jpg

Select all that apply:

x=−6

x=−4

x=3

x=−1

x=0

x=7

To solve the problem, we need to find the \(x\) values where \(f(x) = -3\), based on the provided graph.

### Analysis:
The red curve represents the function \(f(x)\). We are looking for points on the graph where the \(y\)-coordinate is \(-3\).

1. Locate \(-3\) on the \(y\)-axis (vertical axis).
2. Draw a horizontal line from \(y = -3\) across the graph.
3. Identify where this line intersects the red curve (the graph of \(f(x)\)).
4. The corresponding \(x\)-coordinates at these intersection points are the solutions to \(f(x) = -3\).

### Observation from the Graph:
By examining the graph:
- The horizontal line at \(y = -3\) intersects the curve at \(x = -1\) and \(x = 3\).

### Conclusion:
The correct answers are:
- \(x = -1\)
- \(x = 3\)

These are the values of \(x\) for which \(f(x) = -3\).

Do you want more details or have any questions?

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**Related Questions:**
1. What is the vertex of the parabola \(y = f(x)\)?
2. What are the roots of the function \(f(x)\)?
3. How does changing the \(x\)-coordinate affect the \(y\)-coordinate for a quadratic function?
4. What does the symmetry of a parabola tell us about its roots?
5. How would the graph change if the equation were \(f(x) = -2\) instead?

**Tip:** When solving for \(f(x) = c\) using a graph, always look for the \(y\)-value of \(c\) and identify the corresponding \(x\)-coordinates where the curve intersects this horizontal line.

Discover how to find solutions for f(x) = -3 using graph analysis. This problem involves identifying intersections of the function graph with a horizontal line at y = -3. Suitable for high school students.

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