1. **Problem Statement:** Find the x-values where the function $f$ is discontinuous based on the described piecewise graph. 2. **Understanding Discontinuity:** A function is discontinuous at points where it has jumps, holes (open circles), or breaks in the graph. 3. **Analyzing the Graph Description:** - There is an open circle at $x = -4$ indicating a hole. - There is a filled dot at $x = -1$, so the function is defined and continuous there. - At $x = 0$, there is a filled dot, so continuous at 0. - There is an open circle at $x = 2$, indicating a hole. - There is an open circle at $x = 4$, indicating a hole. - The function runs horizontally from $x = 4$ to $x = 6$ with no breaks. 4. **Conclusion:** The function is discontinuous at the points where there are open circles (holes), which are $x = -4$, $x = 2$, and $x = 4$. **Final answer:** $$\boxed{\text{Discontinuities at } x = -4, 2, 4}$$