1. The problem asks to find all the $x$ values where the function $f$ is discontinuous based on the described piecewise graph. 2. Discontinuities occur where the function has jumps, open circles not connected to filled points, or isolated points. 3. From the description: - Top-left quadrant: There is a descending linear segment ending at an open circle near $x = -2.3$, indicating a discontinuity at $x = -2.3$. - Top-right quadrant: There is an open circle near $x = 1.5$ at the end of an ascending curve, so discontinuity at $x = 1.5$. - Another open circle near $x = 4.5$ at the end of a descending curve and start of a horizontal line, so discontinuity at $x = 4.5$. - An isolated filled point at $x = 2$ also indicates a discontinuity since the function is not connected there. 4. Therefore, the function $f$ is discontinuous at $x = -2.3$, $x = 1.5$, $x = 2$, and $x = 4.5$. Final answer: $$x = -2.3, 1.5, 2, 4.5$$