Let’s solve the given problem step by step:

Task

The question asks us to use the graph to determine the $x$-value(s) where $f(x) = -3$.

Step 1: Understanding the Graph

The graph of $f(x)$ shows a curve with peaks and valleys. The value $f(x) = -3$ corresponds to the horizontal line $y = -3$.

Step 2: Locate Points Where $f(x) = -3$

Looking at the graph, $f(x) = -3$ occurs at the following $x$-coordinates:

1. $x = -8$
2. $x = -2$

Final Answer:

If $f(x) = -3$, then $x = -8$ or $x = -2$.

Would you like further explanation of any part of the solution?

Additional Questions:

1. What is the significance of multiple solutions for a single $f(x)$ value in this context?
2. How do we determine the domain and range from the graph?
3. Could we identify the local maxima or minima of this graph?
4. What happens if the graph intersects a given $y = c$ line at no points?
5. How can symmetry in a graph affect solutions?

Tip:

When solving graph-based problems, always check carefully for all possible intersections between the graph and the given horizontal line.