To determine the $x$-values for which the function $f(x)$ is discontinuous, we need to identify points on the graph where there is a break, jump, or any other kind of interruption in the curve.

From the graph you provided, it appears there are two distinct discontinuities. Discontinuities typically occur at:

1. Jumps: Where the function suddenly "jumps" from one value to another.
2. Asymptotes: Where the function approaches infinity or negative infinity.
3. Holes: Points where the function is undefined or not connected.

From the graph, the discontinuities seem to occur at the following $x$-values:

• At $x = -3$: There seems to be a jump discontinuity. The graph breaks and jumps from one point to another at this value.
• At $x = 1$: There seems to be another discontinuity. The curve has a break or sudden change in direction at this value.

So, the function $f(x)$ is discontinuous at $x = -3$ and $x = 1$.

Would you like further explanation on this or have any other questions? Here are some related questions you might consider:

1. What are the types of discontinuities?
2. How do we mathematically define a jump discontinuity?
3. What conditions must be met for a function to be continuous at a point?
4. How can we find discontinuities algebraically?
5. Can a function have an infinite number of discontinuities?

Tip: When analyzing a graph for discontinuities, always check for breaks, jumps, and undefined points.