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.