Based on the graph of $y = f(x)$ shown, we are asked to find all values of $x$ where $f(x) = 0$.

From the graph, $f(x) = 0$ when the curve intersects the x-axis. Let's observe the points where the curve crosses the x-axis.

The graph crosses the x-axis at three points:

1. $x = -7$
2. $x = -3$
3. $x = 3$

Therefore, the solutions to $f(x) = 0$ are:

$x = -7, \, -3, \, 3$

Would you like a more detailed explanation or clarification on any of these steps? Here are a few related questions you might find interesting:

1. How can we determine the number of real roots of a function from its graph?
2. What is the significance of the x-axis intercepts of a function in relation to its zeros?
3. How can we find the exact x-values where a polynomial intersects the x-axis using algebra?
4. How would the graph of a function change if one of the roots was a double root?
5. How can the behavior of a function near its intercepts help determine the nature of its roots?

Tip: When solving for the roots or zeros of a function, it’s helpful to first identify where the graph crosses the x-axis. Each crossing point represents a root of the function.