1. The problem asks to find all values of $x$ in the open interval $-9 < x < 9$ where the function $f(x)$ has a jump discontinuity. 2. A jump discontinuity occurs at a point $x = a$ 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, i.e., $$\lim_{x \to a^-} f(x) \neq \lim_{x \to a^+} f(x).$$ 3. From the graph description, jump discontinuities are indicated by points where there are open and filled circles vertically aligned but not connected. 4. The graph shows jump discontinuities at approximately $x = -3$ and $x = 7$. 5. Both $-3$ and $7$ lie within the open interval $-9 < x < 9$. 6. Therefore, the values of $x$ where $f(x)$ has jump discontinuities in the interval $-9 < x < 9$ are: $$x = -3, \quad x = 7.$$