1. **State the problem:** We need to find all values of $x$ in the open interval $-9 < x < 9$ where the function $f(x)$ has a jump discontinuity. 2. **Recall the definition of jump discontinuity:** A jump discontinuity occurs at $x = a$ if the left-hand limit $\lim_{x \to a^-} f(x)$ and the right-hand limit $\lim_{x \to a^+} f(x)$ both exist but are not equal, and the function value $f(a)$ may or may not be equal to these limits. 3. **Analyze the given graph points:** - At $x = -4$, there is a hollow circle at about $y = -3$ and a filled circle at about $y = -2$, indicating a jump. - At $x = -1$, hollow circle at about $y = 0$ and filled circle at about $y = 1$, indicating a jump. - At $x = 1$, hollow circle at about $y = 1$ and filled circle at about $y = -3$, indicating a jump. - At $x = 5$, hollow circle at about $y = 0$ and filled circle at about $y = -1$, indicating a jump. 4. **Conclusion:** The function has jump discontinuities at $x = -4$, $x = -1$, $x = 1$, and $x = 5$ within the interval $-9 < x < 9$. **Final answer:** $$x = -4, -1, 1, 5$$