1. The problem asks to find all the $x$ values where the function $f$ is discontinuous. 2. Discontinuities occur where the function has jumps, holes (open circles), or isolated points. 3. From the graph description: - There is an open circle near $x = -4$ indicating a hole. - There is a solid point at $x \approx -2.5$ and a smooth curve, so no discontinuity there. - There is a solid point at $x \approx -1$ with smooth connection, so no discontinuity. - The function passes through the origin $(0,1)$ smoothly. - There is an open circle above $x = 1$ indicating a hole. - There is a solid point near $x = 3$. - There is an open circle near $x = 4.5$ indicating a hole. - There is an isolated solid point near $x = 1.5$ which is a discontinuity because the function is not connected there. 4. Therefore, the discontinuities are at $x = -4$, $x = 1$, $x = 4.5$, and $x = 1.5$. Final answer: $$x = -4, 1, 1.5, 4.5$$