1. **State the problem:** We need to find the points where the given piecewise function is discontinuous. 2. **Recall the definition of discontinuity:** A function is discontinuous at a point if the left-hand limit, right-hand limit, or the function value at that point do not all agree. 3. **Analyze the graph description:** - At $x = -3$, there is a green horizontal segment ending with an open circle, indicating the function is not defined or does not equal the limit there. - At $x = 1$, there is a red rising segment starting with an open circle, indicating a similar discontinuity. - The blue segment passes through the origin with a filled point, so no discontinuity at $x=0$. 4. **Conclusion:** The function has discontinuities at $x = -3$ and $x = 1$ because of the open circles indicating the function value does not match the limit or is undefined at those points. **Final answer:** The discontinuities are at $x = -3$ and $x = 1$.