1. **State the problem:** We need to find all values of $a$ in the interval $-9 < x < 9$ such that $$\lim_{x \to a} f(x) = -3.$$ This means the function $f(x)$ approaches the value $-3$ as $x$ approaches $a$ from both sides. 2. **Understand the limit concept:** The limit $$\lim_{x \to a} f(x) = L$$ means that as $x$ gets arbitrarily close to $a$ (from left and right), $f(x)$ gets arbitrarily close to $L$. The value of $f(a)$ itself does not affect the limit. 3. **Analyze the graph description:** The graph crosses $y = -3$ at approximately $x = -3$ and $x = 6$, but both points have open circles, indicating $f(x)$ might not be defined or equal to $-3$ at those points. 4. **Check behavior near $x = -3$:** Since the curve approaches $y = -3$ near $x = -3$ from both sides (even if the point is open), the limit $$\lim_{x \to -3} f(x) = -3$$ holds. 5. **Check behavior near $x = 6$:** Similarly, the curve approaches $y = -3$ near $x = 6$ from both sides, so $$\lim_{x \to 6} f(x) = -3$$ also holds. 6. **Check other points:** No other points on the graph approach $-3$ as $x$ approaches them within $-9 < x < 9$. 7. **Final answer:** The values of $a$ for which $$\lim_{x \to a} f(x) = -3$$ are $$a = -3 \text{ and } a = 6.$$