1. The problem asks to determine the x-values where the function $f$ is discontinuous and to specify if $f$ is continuous from the right, from the left, or neither at those points. 2. Recall the definitions: - A function $f$ is continuous at $x=a$ if $\lim_{x \to a^-} f(x) = f(a) = \lim_{x \to a^+} f(x)$. - $f$ is continuous from the right at $x=a$ if $f(a) = \lim_{x \to a^+} f(x)$. - $f$ is continuous from the left at $x=a$ if $f(a) = \lim_{x \to a^-} f(x)$. 3. From the graph description: - At $x=-2$, there is a gap with an open circle at $y=1$ and a filled dot just below $y=2$. Since the function value and limits do not match from either side, $f$ is neither continuous from the right nor from the left. - At $x=1$, there is a jump discontinuity with an open circle near $y=1$ on the left and a filled dot near $y=2$ on the right. The function value equals the right limit but not the left limit, so $f$ is continuous from the left only. - At $x=3$, the function jumps downward with an open circle near $y=0$ on the left and a filled dot near negative $y$ on the right. The function value equals the right limit but not the left limit, so $f$ is continuous from the right only. 4. At $x=4$, no discontinuity is described, so $f$ is continuous there. Final answers: - $x=-2$: neither - $x=1$: continuous from the left - $x=3$: continuous from the right