To solve part (b) of this problem, we need to find the values of $x$ for which $f(x) = -3$ using the graph of $y = f(x)$.

Solution Steps:

1. Identify the Horizontal Line: Draw or mentally locate a horizontal line on the graph at $y = -3$.

2. Find Points of Intersection: Look for the points where this horizontal line $y = -3$ intersects the graph of $y = f(x)$. Each intersection corresponds to an $x$-value where $f(x) = -3$.

3. Read the $x$-Coordinates: For each intersection point, read the $x$-coordinate. In this case, based on the graph:

   • The first intersection at $y = -3$ occurs around $x = -1$.
   • The second intersection occurs around $x = 1$.
   • The third intersection occurs around $x = 5$.

Therefore, the values of $x$ that satisfy $f(x) = -3$ are $x = -1$, $x = 1$, and $x = 5$.

Final Answer:

$x = -1, \; x = 1, \; x = 5$

Let me know if you would like further clarification on this solution or the graph analysis!

Here are some related questions you might explore:

1. How would you find the $x$-values for a different $y$-value, such as $f(x) = 2$?
2. What would $f(x)$ be for values of $x$ that lie between the intersection points?
3. If the function were transformed, such as $y = f(x) + 2$, how would the solutions for $f(x) = -3$ change?
4. How can you determine whether the function $f(x)$ is increasing or decreasing at certain intervals?
5. What does each intersection of the graph with a horizontal line indicate in terms of the function's behavior?

Tip: When analyzing a function graph, always focus on how horizontal lines intersect the curve to identify values satisfying $f(x) = c$.