1. **State the problem:** We are given a graph of a function $f$ defined on the interval $-9 < x < 9$ and asked to find all values of $x$ in this open interval where the function has a removable discontinuity. 2. **Recall the definition of removable discontinuity:** A removable discontinuity occurs at a point $x = a$ if the function is not defined or not equal to the limit at $a$, but the limit $$\lim_{x \to a} f(x)$$ exists and is finite. This often appears as a "hole" in the graph (an open circle). 3. **Analyze the graph details:** - There is an open circle at $x = -6$ with $f(-6)$ not defined or different from the limit. - There is another open circle at $x = -3$. - The graph is continuous elsewhere except possibly at $x=3$ where there is a vertical asymptote or sharp drop, which is not removable. 4. **Check the open interval $-9 < x < 9$:** - $x = -6$ is inside the interval and shows a hole, so it is a removable discontinuity. - $x = -3$ is also inside the interval and shows an open circle, so it is another removable discontinuity. - $x = 3$ is inside the interval but shows a vertical asymptote, which is not removable. 5. **Conclusion:** The function has removable discontinuities at $$x = -6$$ and $$x = -3$$ within the open interval $-9 < x < 9$. **Final answer:** $$\boxed{x = -6, -3}$$